Overview
A helpful guide to Angel Rooms.
What is a Angel Room?
The Angel Room is a special room that was added in the Wrath of the Lamb DLC and can replace any Devil Room on any floor. These rooms will give you a free item with no cost, unlike Devil Rooms. You will know when you get an Angel Room when a door with a cross is above it and is where a Devil Room would be and the sound of some kind of angel choir will be triggered.
Example of a Angel Room from the wiki
Angel Room door after the defeat of Mom’s Heart from the wiki
How can I get a Angel Room?
Angel Rooms can be random, but you can increase the chances of finding one if you are defensive during the boss fight (or don’t take any damage during the boss fight). This increases chances of finding one, but won’t always work. (basically the devil room)
What can I find in a Angel Room?
You can obtain 11 items from the Angel Room.
The Bible: When used, Isacc will gain flight and will instantly kill Mom and Mom’s Heart/It Lives! if used in the boss room. It will kill Isacc if the item is used while fighting Satan, Isacc, and ??? unless you have the wafer.
The Relic: When picked up, Isacc will be followed by a blue cross familiar that drops a Soul Heart every 5 rooms you clear.
Sacred Heart: When picked up, shots will be larger but travel slower and home on enemies. It also Multiplys your damage, restores you to full heath, gives you a Soul Heart.
Scapular: Once per room, when Isaac is reduced to his last half red Heart, the aura around his head that is given when picked up temporarily vanishes and he is granted one Soul Heart.
Prayer Card: Takes up your item slot and when used, it grants half an Eternal Heart.
Mitre: Greatly increases chances of replacing regular hearts with Soul Hearts.
Holy Grail: Adds 1 empty heart container and gives you flight.
The Halo: Increases all states by 1 and gives you an extra heart container.
Guardian Angel: Spawns a Angel that will orbit Isacc like Cube of Meat. It does damage if touches by an enemy, blocks shots, and doubles the speed of other orbitals like Cube of Meat and Attack Flies.
Dead Dove: Gives Isacc flight and spectral tears, similar to Curse of the Night.
Blood Of The Martyr: Increases your damage by 1 and gives Isacc blood tears. If collected with The Book of Belial, the damage will be mulitiplied by 1.5 upon the activation of The Book of Belial.
Note: These items can also be found in item rooms.
The End
There you have it, a quick guide to Angel Rooms. If I missed anything or you found any grammar mistakes, put it in the comments so I can fix it. Hope this helped a bunch of confused people. 
Resources: The Binding of Isacc Wiki. All pictures and info are from the wiki, I own nothing.
