To actually start using the mod, open up the game and click on "Mods". This will bring up the mods browser. It might take a second or two but you should soon notice that any newly subscribed mods will be automatically downloaded and installed.

After the mods are installed, new listings will be displayed for each mod. Click on the checkbox icon to the left of the entry to enable the mod. You can also click on the entry itself to view details of the mod (this can be useful if the mod depends on a specific DLC).

Once you've enabled all the mods you plan on playing with, click next and the mods will be applied. You can then navigate the menus to start up a new single player game or custom game.

Some mods may show an "Update" button. This means that the author of the mod has created a newer revision of the mod in Workshop. Clicking update will delete the current mod from your system and download/install the latest version from Workshop.

You can remove the mod while in-game by clicking on the mod entry and clicking "Unsubscribe" or "Delete. You can also select "Unsubscribe" from the web browser and the mod will be automatically removed the next time you run the game.