The basics of Dodges and Counter Attacks
When you see an enemy beginning his attack animation towards you (pay attention to the enemy: as soon as you see it moving towards you in ANY way...), press SPACE or RIGHT MOUSE CLICK. In case of larger enemies or ranged attacks, instead press the dodge button just before being hit by whatever they are throwing at you. (about 0.5 seconds before being hit is a good timing example).

The result of this action is different depending on the character you are using:

• Jill will perform a fast rolling move, and will be invulnerable from any damage during this animation.
  
• Carlos will instead perform a powerful melee counter, capable of knocking on the ground, or stun briefly all enemies except Bosses. He also becomes invulnerable during the animation.

Slow Motion Counter (Jill Only)
When using Jill, she can perform another special move. After a successful dodge, press the button you use to aim your weapon (default is RIGHT MOUSE CLICK) and hold it down, this will slow down time considerably and also automatically aim towards the weak point of the enemy you just dodged. It's a very powerful move to score a weak spot hit right after dodging.

Strong Punch Counter (Carlos Only)
When using Carlos, after performing a counter attack with him, if you press the dodge button again (so SPACE or RIGHT CLICK) Carlos will perform a special strong punch to the enemy he just countered, slamming it to the ground even more and possibly doing extra damage. Also, this can be done even if you fail the timing of your initial counter, press the dodge again after you failed the timing and Carlos might execute the special punch immediately, countering the enemy even if you failed the first time.
- Credits to Jeronimous for this suggestion.

Free Punch (Carlos Only)
The Strong Punch can also be executed without having an enemy close by! To do this, press the dodge key, wait half a second (so at the end of the initial counter animation), and then press the dodge key again. It’s all in the rhythm, but it means that you can initiate a punch from a further distance if needed if you aren’t confident in countering.
- Credits to i-ghost for this suggestion.

About Reliablility and Timings
In my personal experience, Jill's dodge is reasonably reliable and works most of the time. The same cannot however be said for Carlos' melee counter, which is prone to just not working for seemingly no reason, even with a perfect timing. My suggestion is to stay as safe as possible with Carlos and use his melee counter only when you have no choice and are in deep trouble - it's not reliable enough to use frequently.

Advanced Side Grab Deflection
There is another type of dodge you can perform. It can be only used against side grabs, or grabs that are not too direct. That means, if you are "passing by" a sombie on the side, and it tries to grab you, then you can perform this move. But instead if you have a zombie in FRONT of you, and it tries to grab you frontally, this will NOT work.

To perform the Side Grab Deflection, you need to press the movement direction OPPOSITE to the grab at the last moment before being grabbed. By doing this, your character will push away the zombie and evade the grab.

Refer to the following video for more explanation (the video is from RE2 Remake but it works THE SAME WAY). LINK: https://www.youtube.com/watch?v=rvlUpjaKTd8
- Credits to Imanodesu for this suggestion.

Item Highlighting
If you pass close enough to an item you can pick up, it will be marked on your map permanently - even if you didn't "see" it yourself. However you need to pass close enough to it (about 3 meter radius), else it will stay hidden and will not be on the map. This does NOT work for breakable special statues, they will be always hidden even if you pass very close to them.

Red Zones and Blue Zones
The map will actually tell you if there still is some item to find in a specific area. Each map is divided in various zones, and they can be RED or BLUE in color. RED color means there is still an item to find in that section of the map, BLUE instead means that section is 100% clear of anything you can pick up. This function is very useful to be sure you got everything. This does NOT count breakable statues, so an area can be BLUE even if there is a statue to find in it.

What are you talking about here?
In RE3 and also other survival horror games, some enemies and especially bosses have some "phases" when they suffer much LESS damage. Now i'll explain you how to understand this and save precious ammo.

Non-Boss Enemies
Regular zombies (with clothes on, to be clear) will suffer reduced damage while they do a falling animation, while they convulse on the ground after being shot the first time, and also while getting up from prone. If you shoot them in any of these phases you will deal reduced damage, or no damage at all.

Other "special" enemies to my experience don't have these frames however some have certain "forms" where they suffer MORE damage, otherwise damage would be regular. Of course no spoilers, so i will leave them to you to find out.

Applied to Bosses
With bosses it's a much deeper affair:

Generally the rule of thumb is: if a boss suffered enough damage to be staggered, then you should wait for him to recover from the stagger animation before shooting him again. In my experience if you shoot a boss while he "recoils" from heavy damage, you won't have the same effectiveness.

This "rule" is only to be followed when the boss recoils as a consequence of your direct attacks to him, and NOT special actions (such as shooting a particular piece of machinery, for example) which instead are intended in the boss fight mechanics and are, contrary to what said before, intended for you to shoot at him while stunned. Since no spoilers here, it will be up to you to understand this difference.

When a boss changes form or phase, it's usually recognizable as the boss will change shape, form or do some very explicit act to symbolize he is "powering up". During these phase bosses are INVULNERABLE. So give them their time to channge to their new "form" and AFTER that, when you see the bad guy moving around with murderous intent... that's when the pummeling starts again.

Making sure zombies are really dead
Just because you see a zombie drop after some shots in the head, it doesn't mean he's dead for good. In fact most of the time he won't be, and get back up again after a variable time.

Against single zombies, as soon as you drop them after multiple headshots, equip your knife and stab the fallen zombie in the head multiple times. After one or two stabs (or swipes wich Carlos) the zombie will move again: keep hitting him in the face with your knife and generally 3-4 hits will be enough to put it down for good.

Downed zombies that are still alive regenerate themsleves, because of the virus, and come back up at nearly full health to bother you again. So doing this will save you a LOT of ammo and possibly damage.

BE CAREFUL! Some zombies are more resilient than others and while you try to stab them as described above, you will not be able to kill them in time and they will attack you again instead.

You can however understand when this is the case: if a zombie is downed with very little health, after a couple knife hits it will perform an animation where he lifts an arm like grasping to the air, and then fall soon after - that's the "true death" animation. If the zombie instead stands up with its whole torso or tries to get up from prone, that means it has still some life in itself and you'll need a couple more bullets to get the job done.

These "tougher" zombies are completely random and more rare than your average zombie, there is no way to tell they are tougher or not, however.

Exceptions

• Zombies killed by a barrel explosion will NOT get back up. They're gone.
  
• Zombies whose heads explode as a result of heavy weapons or a lucky shot, are gone for good.
  
• Zombies who fall while ignited from fire will not get back up. They are burnt to a crisp.
  
• Zombies killed by heavy explosions such as grenades, will be dead for good.

Recovering faster after being knocked down
It seems that if you "spam" (press a lot of times, very fast) the movement key and the action key (so WASD and your assigned action button) will make you recover faster than normal from any stagger / stun / knockdown.
- Credits to Jeronimous for this suggestion.

Extra weapon damage
If you wait for the aiming reticle to become fully "closed" (it becomes smaller the more you aim, until it's "closed"), and then shoot your weapon, the resulting attack will inflict extra damage compared to one performed when the reticle was NOT fully "closed". This info is also written in the official game manual.
- Credits to Jeronimous for this suggestion and updates.