Both Kyle's Custom Character Mod and Mod the Gungeon are crucial for installing mods.
Install the Custom Characters Mod, by placing it, zipped, in the mods folder of your Enter the Gungeon directory, commonly found at "C:\Program Files (x86)\Steam\steamapps\common\Enter the Gungeon". Delete mods.txt if it is present.
Launch the game. This will create a folder in your Enter the Gungeon directory called CustomCharacterData. If it does not appear, it has been installed incorrectly.
Place the character's folder inside the CustomCharacterData folder, then launch the game up again. The console will show a list of available characters, and up to 21 characters can spawn in the breach if all was done correctly.