If you install mods before you have defeated Mom (the first time on that save file), the game will lock your achievements. You will still get the item, but the "Mom's Heart" kill won't count toward progression.
If you are playing Repentance (the final expansion), the Steam Workshop is seamless. However, if you are playing the older Afterbirth+ , you have an extra step. You must enable the "Enable Mods" button in the Mods menu.
This is the step everyone forgets. Subscribing does turn the mod on automatically.
No official in-game mod menu. Mods must be installed manually.
Launch the game. A "Downloading Mods" screen will appear as the game syncs your subscriptions.
But before you turn this game into a psychedelic fever dream, you need to know the rules of the road. Here is your step-by-step guide to downloading Isaac mods without breaking your save file.