Bethesda have announced during a livestream that Fallout 4 mods that feature on Xbox One cannot be any larger than 2GB in size, along with other details outlining the process of installing.
Mod sizes vary, but on console, they will never exceed 2GB. They can be easily deleted if you have to free up space.
Bethesda also discussed the process of installing and activating mods. You mods can be found in the “Mods” menu, naturally, once your account has been linked to your account on Bethesda.net. From there, you can browse all available mods then download and install them directly on your console. The current mod collection can be found here.
When you use mods, you automatically start a new save. If something goes wrong with the mod and you lose progress (the game crashes or some other technical error), you can revert back to your regular, non-modified save game.
Due to first-party consideration, achievements will be disabled while mods are installed. The only way to reactivate achievements is to delete all installed mods. Also, in similar fashion to The Sims custom content, mods which capitalise on the content of DLC packages will only be available to those who own the DLC.
It is unclear whether the same restrictions will apply on PlayStation 4. Mods will be available on Xbox One on May 31 and on PlayStation 4 sometime next month.