Steam will show you the progress like if it was an update to the game.
Once you are subscribed to it and start the game, it will download the MOD, it is fairly big, about 800MB. To get the MOD, search on the Steam Conan Exiles Workshop for the MOD called Dark Desires and subscribe to it. Bonus points if you pick the exact point where that begins! The Age of Calamitous Best Conan Exiles Mods.
Note, this list of Conan Exiles mods will contain some adult themes and NSFW content.