Before even thinking about the mines, consider the following tips:
ALL offensive staves work.
It doesn't matter what their beatitude is. Even if they ingrain themselves onto your hand, they will still deal plenty of damage!
Plus, staves break easily. They go down in quality after a few shots, meaning that if you don't want a staff to be stuck to you, it will eventually degrade enough to the point they will automatically remove themselves from you.
Cursed beartraps are always useless. They break instantly upon deployment, so no need to hold onto them.
I hope you have accostumed yourself to the dark!

You usually want to have a ring of warning at this point.
If you don't have one, a ring of invisibility (very lucky!) can help a bit.
If you happen to have any magic reflection cloaks or amulets, equip them! Most gnomes have lightning staves.
If you found beartraps, they will be very useful.
Any offensive spells will help. Early in the game, staves (of any beatitude) are the most reliable.
Any ranged weapons can help a little.

If you got lucky and found a tinkering kit early on, or you happen to be a mechanist, good job!
Mechanists and rogues start with the tinkering skill at 40 proficiency.
Beartraps (craftable at 20+ tinkering) prove themselves to be a good tool for keeping enemies stuck in a spot for several seconds.
Simple sentries (40+) are weak and slow, but they can dispatch a gnome in a few shots. They don't fare well when dealing with a crowd of enemies.
Complex sentries (60+) are even better, as they fire faster, their bolts are slightly stronger, and can withstand a few troll blows.

Make as many sentries as you can deploy (usually 4), then spend the rest into beartraps.

If you're a mechanist, by this point you should have somewhere between 40 and 60 tinkering and plenty of scrap to spend. You can make spellbots, but they will be frail.

Enemies will target you immediately if they can see you, and they will see you if they enter the starting room. Thankfully, no enemies are within this room, but they are close by, and they will start moving into it in a few seconds.
Therefore: As soon as you enter, take down all torches!
The fountains can wait - Don't drink them yet. (If you get unlucky and paralyzed, gg)

If you've got any light source on you, get rid of it. Lanterns, torches, even the light spell.
If you've got beartraps, start arming them in front of the doors. It's most optimal to place one per door if you have the resources. Got more? Place more!
If you've got sentries, place them! One per corner is ideal. Complex sentries would be best.
If you've got a dummybot... I don't usually place them, but they can help draw attention away from your sentries, allowing them to last longer.

You might want to keep the doors closed. Gnomes can simply open the doors, but trolls will have to spend some time knocking on the door to break it.
Opening doors makes noise, alerting you of anything coming your way.

After that, just go into a corner and wait.

And so comes the hardest (or easiest, depends on who you ask) part of the floor: Surviving.

The best strategy so far is just to chill on a corner of the starting room. Specifically, a corner furthest away from the doors. That way, you are able to watch the entire room for any incoming evildoers and be able to scatter if something goes wrong.
Standing at the center of the room gives you a significant blind side that enemies can use to sneak next to you and pulverize you.

If any enemy dares to show their ugly face across a door gate, attempt to kill them.
If you can help it, avoid engaging in melee combat! You are somewhat weak at this point, and getting hit by lightning or punched by a troll can mean certain death for you.
Some gnomes will drop their lightning staff. Their beatitude ranges from +1 to -1, but for the purposes of surviving the floor, pretend all staves are of the wrong beatitude for your race and equip them anyways lol. Make use of them!

If you need to engage in melee, actively avoid any enemy you can't kite.
Lightning gnomes are obviously a bad idea, and trolls can usually two-tap your squishy body. That leaves pickaxe gnomes!
Their melee attacks don't particularly deal big damage (unless you are rather weak), thus they're the perfect target for bruising.
Though... if you can kite all enemies, then by all means, go for it. Watch your back for any funny enemy getting in the way though.

There are gnomes that spawn with a lantern. If they come to the room, they will cause all enemies to be able to see you.
Try to kill the gnome with the lantern first.

Avoid leaving the room until after several enemies have been killed or a few minutes have passed.
The maze can be dangerous as you might not know what's hiding behind a corner or even sneaking up behind you.
You might not notice a troll sneaking up and trapping you between another troll!
But if you need to explore the maze early on, take a pickaxe of any beatitude with you first. If you manage to get stuck between enemies, equip the pick and hack walls away!

If you get bored of waiting, or you feel like it's safe to explore now, go ahead!
If you haven't used the fountains yet, you might want to bottle the contents up instead of drinking the water.
You might want to take some staves with you to quickly destroy anything in your path, and pickaxes to get rid of some walls.

If you can craft a noisemaker, you can use them to lure remaining (nearby) enemies to be picked off by you or any deployed traps/sentries.

Note that if you do this early, you will cause a crowd of enemies to beeline towards the room, which is pretty much a bad idea. It's better to do this when the number of enemies have diminished, otherwise your sentries may be overcrowded and smashed before they manage to do serious damage.

This will net you some good experience and tinkering proficiency!

This floor has some loot for you to discover:

Plenty of gold. Almost every dead end contains a bag of gold, free for the picking.
Assorted items. Some dead ends have chests. There are four chests to find!
There is a shop at the top-right corner of the map. It has a lever that opens something...
At the bottom-right corner of the map, there is a podium holding the Sphinx's Veil. Unfortunately, it is surrounded by traps and locked behind gates. But if you happen to have pickaxes or have pulled a particular lever...
The exit can be found at the bottom-left corner of the map.

That's about it.
This is kind of my first guide, so I hope this helps you out!