Learn to dodge!
One basic key to surviving in TboI is learning how to dodge properly. The game will become much easier once you learn how to dodge properly, and this works great in combination of circle strafing (moving in a circular or counter-circular direction while continually firing).
You can also use solid objects such as rocks or poop as shields against your enemies, and even lure enemies onto hazards such as spikes or fires.
Having an item that allows you to hover (including the Bible and Hanged Man tarot card) can protect you from melee hits if you stand over a gap. Keep them in high priority of getting, especially in later floors. If you have the Ouija Board as well, you can fly over a rock and be immune to non-piercing projectiles. You can also use this (or a bomb or ladder) to cross a gap to reach treasure chest/drops.
Rooms
It's usually a good idea to clear the room of any breakable objects (poop, fires, etc) or to keep a mental note of a point of interest; such as an arcade or golden chest. It's also advisable to fill completely out the floor map. However, in later floors: Be wary, as you can encounter the deadly sins (sometimes a super variant) or a mini-boss.
Rooms (Secret Room)
The secret room is usually contained in the area where a room has the most exits, at least three and never four. Once you find a few secret rooms on your own, their locations are pretty easy to guess.
If you have bombs to spare, not enough keys, and if the room you want to gain access is adjacent to a secret room; you can bomb into the secret room and then into the room you want access into. The door will unlock too.
Rooms (Arcade)
Blow up the shell switching game first if you have any bombs unless you have the Lucky Foot or are playing as Cain. This is because the odds of winning are very low without either. If you have either though, you should try getting the Skatole.
Next, do the slot machine. Put in as many as you can or until it blows up. Got a dollar bill? Awesome. Dollar Bill+Steam Sale=WIN
As for the blood machine, just use it the amount of times equal to spare hearts you have lying around. Then, use any coins you have left on the slot machine if it's still there and blow it up once you're done.
Rooms (Gauntlet)
I usually find the gauntlet rooms not worth the trouble if it's just a normal chest. However, if it's a good item or golden chest; go for it. You can also bomb into a gauntlet from an adjacent secret room, steal the loot, and then exit through the bomb hole.
Rooms (Devil Room)
When you defeat a boss, the Devil Room may open if you take no damage during the boss fight, kill a beggar, take no damage on a full floor, or acquire a demonic item. It's worth going in for window shopping (and shooting out the fires) but since you are paying with portions of your own max-health, you're taking a big risk unless you have plenty of max-health.
Beggars
If you see a beggar, give him any coins you have. He usually gives good items (usually a max-health boost item) and the chance is higher if you give him your last coin. These guys are lifesavers, especially in The Womb.
Items and such
I think, one of the most important upgrades are more max health. You should pick up any max health upgrades you can find if possible. On a somewhat related note, you can use items that grant invincibility to milk blood donation machines without losing any hearts. You should however, leave soul hearts until the boss or if you're in dire need of health.
The next most important upgrades are from the treasure rooms. Even if you're in dire need of health, make finding them a high priority as soon as you get to a new floor.
If you have only one key, you should almost always save it for the treasure room. Especially true early on during runs, such as Basement F2, and the early Caves floors.
Conserve your coins unless you have a fairly large stockpile. If you have a spare key though, it's worthwhile to check out if there are any good items. On sale, or a Steam Sale item? Even better. Steam Sale item available, AND on sale? Fantastic.
Conserve your bombs for finding secret rooms, X marks the spot rocks, and bombing slot machine and blood donation machines. You can also use bombs to escape from a room while in combat, but this doesn't work with doors that require a key.
