Especially on higher difficulties (which are quite an endurance test), you should try to stay alive and take as little damage as possible. That means abusing the small time frame you have when you pop out of cover, get hit and lose armor (but not health) to make the best you can out of it, such as marking a special unit, killing cops or just peeking. Also means that you should try to, if possible, seek new cover in order to wait for the armor to recover. Even if you suck at doing this, over time you´ll be better and faster at doing this.
Also, it means making harsh but rational decisions, such as leaving a teammate to die, if the risk is too great (better 1 person gone than 2). This is especially true on public games (not with your friends or people you know), where it´s usually "every man for himself".

"Each team needs a leader. Listen to him. Do what he says. If he's an idiot you still can choose not to listen, but because you've checked his profile you know if he succeeded this heist in the past or not."
Dussel

Every team needs a "Real Life Dallas" to coordinate things. If there isn´t one, you should assume that role; if there´s more than one, you should reach an agreement or just disband (or worse: each act independently and hope for the best). What SHOULDN´T happen is nobody talking anything, the heist failing and people arguing or leaving, stressed out (when that happens, they have no one to blame but themselves, since this IS a multiplayer game). Nobody likes to fail.
Even when you don´t feel like talking (e.g. you had a bad day), you should at least say some basic things (on mic or just typing) regarding the plan.

If you´re not playing with friends, make sure everyone can understand you, as there are a lot of players from different countries playing this game (some of them don´t even speak or understand English).

If you have a plan, then you have a role. Do that poorly (aka run around alone and die at ♥♥♥♥♥♥ spot or take a lot of damage) and you´ll suffer, your teammates will suffer, and ultimately you could lose the game. Do not underestimate the ability of this game in screwing you up, because it most likely will, and then you´ll have no one to blame but yourself.
This may sound obvious, but it isn´t, and is something that unfortunately is learned through experience. BAD EXPERIENCES.

Mark every special cop that you see, especially the one that just murdered you or is in the process of. That way, your friends can avenge you and/or help destroy this menace.

Got smoked? Are bored? Keep spamming "F" (yell/mark) - it will do more than just annoy your teammates (don´t mind them): you can detect cops through the smoke (including SPECIALS) and it can keep you always on top of your game (think of it like a way to make sure your attention is in the game and you´re ready for anything - professional e-sport players all the time: they do a lot of actions per minunte, even though redundant, to stay sharp).

So, you got tased and managed to hit the taser and set yourself free for... 1 second. What to do with that 1 second? Finish what you started: one of you is not going home (he will, at least, not let you do that). Run only if you´re sure you can get out of his sight on that time frame.
Alternatively, you could walk and shoot him (preferrably in the head to stun him) in order to prevent his tasing, thus making it possible to escape.

Test it yourself: reloading with an empty clip is slower than with an almost empty clip. It saves time, especially if a Dozer is coming.

After popping out of cover to shoot at enemies and popping in (after getting hit) and your clip is low or something menacing is approaching (aka Bulldozer) or you just feel like, you´ll often find yourself reloading a half-empty clip just to get the clip full. But what if some enemy pops out of nowhere? Then you should sprint (by default set to Shift button + a directional movement) a little bit (like, 2 inches, 0.1 second) to cancel that reloading process and make yourself ready to fire. It´s faster than switching to a weapon and back.
You can also use the melee button for that purpose, but it´s slower.
This also works to skip the end animation of the shotgun reload (thanks Nirvash, for the tip!).

Mostly you´ll want to use this for escaping. Especially Cloakers, since they run slower than you.
Or to cancel reloading (just sprint for a very brief moment).

If you´re camping a spot, you should keep track of special units in the area. If you´re on the run, ocasionally look back to check if there are cloakers or any other threats.
You should always have a general idea of where the "cop deathball" (most of the cops) is and where they´re spawning from. Sometimes it´s easy to see, other times it´s just experience (finding out on other playthroughs and memorizing the spots).
Also, especially in pubs, make sure that whatever you´re doing is NOT REDUNDANT, as it CAN AND WILL hurt your team (aka 2 or more people restarting the drill or getting a person up instead of covering the teammates and then surprise Bulldozer or Cloaker appears). This game is merciless and will punish you if it finds a chance.

LOOK AROUND YOU if you´re alone and are about to do something that requires your focus and makes you vulnerable, such as getting someone up, restarting a saw or trading a teammate. Did a Cloaker see you or follow you? Which direction the cops are coming from, and what´s the best cover against them?

Unless the team is using a specific strategy which requires not taking hostages at specific points, you SHOULD take hostages (preferrably cops, if you know that at some point later you´ll find civilians). Civilians should be tied in a spot where they will be safe from harm (aka GL40 shots) and also hard for cops to reach and set them free. Preferrably a place with some cover.
There are 3 types of cops that can be "hostaged" and you SHOULD MEMORIZE how to do it with each weapon that you use often. That way, it´s gonna speed up the process and free your thoughts whenever the situation calls it, especially during those 30 seconds between assaults (which happen too fast and require you to deal with leftover special units + regular cops in groups AND get hostages to trade for teammates).
For instance, I memorized that on Overkill 145:
- I should spam "F" (scream at the cop to surrender) on a cop after the assault to check if he´s wounded and wants to surrender (sometimes fails)
- cops in groups of more than 2 will have a greater chance of not surrendering
- it takes 1 headshot from 308 for the heavy swat to want to surrender, and 2 melee hits on blue swat and fbi cops

Also, consider sending teammates to die and trading them back if they´re low on ammo and the ammo bags are almost or totally gone. It may be kind of cheesy but, hey, you WANT to win, right? (Without hacks of course; otherwise, DUH!!!)

Every team, especially on Overkill and above difficulties, should have at least 2 people with the "Big Game Hunters" (BGH) crew bonus. For equipment, everyone should have "Extra Start Out Ammo" (unless you´re the "objectives man" on specific strategies). Both give extra ammo at the start and increased ammo capacity. This way, you can almost double the total ammo you have to spend. MUST HAVE if you want to play safe (especially in a game which requires so much patience as Payday).

Each ammo pickup that a cop drops will fill up a little bit of the 3 weapons that you have. You SHOULD have a general idea how many are replenished and spend your ammo wisely before collecting more (not to mention knowing HOW MANY to collect). Your primary weapon should be used for taking out specials (mainly Dozers) and/or clearing a lot of enemies fast. Use your secondary as much as possible.

Always go for headshots, especially against heavy swats and special cops.

You should, whenever possible, choose a proper place for the cop to die, in order to make it easier to retrieve the ammo (for example: behind nearby non-cop-infested cover, or at point-blank distance). This also takes into account the fact that ammo pickups have a cap (past a specific number, no new kills will spawn ammo pickups as long as the ones on the ground aren´t picked up). In other words, DON´T KILL COPS YOU CAN´T SLAP OR STEP ON.
A good way to do this is to kill a cop at point-blank with a Bronco headshot - as soon as the enemy drops the ammo is picked up, giving you a positive ammo trade.

Depending on the strategy, you´ll find yourself doing ammo conservation (weapon cycling + proper kill placement + looting ammo pickups) or simply spamming your main weapon and using the ammo bag to keep it stocked up with bullets. It´s about how aggressive you´re going to play or the situation demands.
Each ammo bag has a limited number of bullets (that´s how it gets spent, and NOT by number of uses): it´s equivalent to NINE FULL CLIPS OR SO. So, if you´re running low on ammo (in specific situations, 50% is a low amount) and has no other way to replenish it or the situation demands it, use the ammo bag. Better safe than sorry.

If you get the chance to shoot it far away, do so. When it´s nearby, just UNLOAD on his faceplate (the FRONT GLASS). Especially if he has already fired his shotgun at his target and that target is exposed for the second one. Especially if everyone else is doing the same (shouldn´t take longer than 2 seconds for him to fall). If you´re using the 308 or the AK and isn´t his main target, you have an obligation even greater, since 1 full clip is enough to kill it (if it were only you, you COULD SOLO).
If you´re alone or the main target and feel like you´re not going to fully unload before the second shot (like, you missed a few shots or your left mouse tapping is slow for some reason or your teammates in a public game aren´t cooperating), hide. "Staying alive is a priority".

It´s better to kill them on sight. Even if they´re far; don´t waste opportunities to kill them. Show no mercy when they´re downed on the ground and keep shooting them, preferrably in the head.

Shield: shoot the shield with a GL40 or get behind it or use Crossfire setup. When in a cramped up space (e.g. a camping spot with 1 doorway), try to have someone make him face away while someone else gets real close to him and shoots him from the very small gap created.

Cloaker: know the map well to know where he can spawn, look around you (mind your surroundings; if you hear a machinegun which sounds a little quieter and/or get hit very fast by a machinegun, beware - it could be a Taser/ Cloaker/ Murky). Shoot him in the head (on Overkill, for instance, it takes 2 shots from a 308 to take him down - double tap works on close/medium distances and can dispatch him very quickly). If you see one on your path, don´t get close to him, EVER. If you see one running in your direction and you have no ammo, run and mark him, so someone can help you.

Bulldozer: shoot him in the faceplate. You should pay a lot attention to the shotgun sound, so you can time it properly and avoid getting damaged badly. If you can, make him chase you - sometimes he will pop out of a corner missing the shot (firing too early), so you´ll get a lot of time to take him down. If he surprises you and your teammates, mark him, see if everyone´s gonna fight him or not and act accordingly (when in doubt, just unload on his face; especially if you didn´t get hit yet).

Taser: preferrably shoot him in the head (including sadistically shooting his head while he´s down on the floor) . If you hear an acute sound (of the tasing gun) or if you see some blue sparks, beware (the best way to counter this is memorize his position, then popping out of cover immediately shooting his head). When you´re getting tased, in general try to center the aim on him and press the firing button (left mouse, by default) - it may spend your ammo faster, but it increases the chance of hitting him and freeing yourself.

Always prefer to shoot while standing still. While on the run, though, sometimes you´re blocked by cops. A good way to deal with this is using "Stutter Step" (watch video on how to do this) to stop yourself momentarily and at that moment shoot, then go back to moving again. This applies to movement in all directions. You don´t have to be as precise as in CSGO.
You can also use this technique to pop out of cover and stop and fire as soon as you see a target, then rinse and repeat. Works really well with Bronco.










Also, an easier way to fully stop momentarily is to aim down the sight (by default it´s set to right mouse button).

It depends on the strategy and the situation. If you´re camping at a spot with at least 2 other members, you CAN afford to do use the medbag only after going down twice. However, you should evaluate the situation carefully:
- is the map a quick one or are you abandoning the camping spot for good? Heal if nobody else needs it more than you (unless you know there´s enough charges for everyone)
- the "leader" told you to do so? Heal
- are you alone or with only a teammate, with health on red and you´re supposed to survive the cop assault? Heal
- are you the "objectives man"? Heal

If you´re healing more than once in the same assault, I guess you should evaluate how well you´re playing. Are you taking too many risks? Or did you get unlucky with a special unit despite all cautiousness?

When camping a spot, it´s better to have a Crossfire (a position where 2 players can face each other so that whenever an enemy shows up, he´s gotta face one of the players, leaving him vulnerable to the other player). Basically for taking out Shields without the GL40, but works well against all cops.

A better way to explain this is looking at this picture: imagine 1 person in each room, and a shield coming from the hallway.