How do I find secret rooms?

Look for walls that have no other rooms close to them (to make room for the secret rooms) then shoot them with a non-starter pistol. Cracks may appear with light shining through, that is when you use your blank to open the passage. If enemies explode near the wall it also may reveal cracks. Don't forget, secret rooms may also appear in chest rooms but never boss rooms and dont look too hard for them since they sometimes may not even be worth the ammo spent looking for them.

Revising this answer as the previously listed method does not work.

Guaranteed Methods of Finding Secret Rooms

The items Brick of Cash, Map, Gungeon Blueprint and the Insight synergy will all show you exactly where secret rooms are located, either by showing it on your map or by having a small creature spawn near the entrance of the rooms. Of course these methods require you being lucky enough to find these items.

Strategies for Secret Room Hunting

If you have a weapon with limited ammo, your best bet is shooting the center of each wall in chest rooms and around the exit elevator room (though not on the center of the side walls, example shown below).

If those rooms don't reveal any cracked walls, it's also often worth spending a blank in the shop before finishing a floor, assuming there's space around the shop to allow for a secret room.

Other than that, be sure to take a quick look around room after a firefight (particularly dead end rooms), and keep a blank (or Bomb/Lil' Bomber/Elder Blank) ready to open it up when you see it.

Happy hunting!

Chest rooms have a better chance of having secret rooms, also the shopkeeper has the ability to sell maps, and check the map, to make sure you dont try to find a secret room but there is another wall nearby that wall!

There is also a way to tell in a wooden/library chest room. There is an obvious space with no books where a corridor can be.