This guide will show you the different ways to add mods to your server.
Mod portal (website)
Factorio's developers created the mod portal (website) to allow the players to share mods. A mod you download from the website comes in the form of a zipped file. To install the mod, you need to copy the zipped file into the mods directory located under the user data directory without unzipping it. You can verify whether or not you installed it correctly by viewing the mods list which you can access through the game's main menu.
Mod portal (in-game)
The mods displayed on the mod portal (website) should show in the in-game mod portal which you can access through the game's main menu. The differences in the in-game mod portal are that you can use it to both automatically download and install mods, and to enable or disable the mods.
Mod subforum
Some mod creators upload their mods to the official mod subforum to showcase their work without submitting to the mod portal or to get feedbacks from the community on their mods before updating or sending them to the mod portal. An uploaded mod should show as an attachment. Occasionally, a mod you download from the subforum comes in the form of a zipped file. You need to copy it into the mods directory located under the user data directory to install it — you do not have to unzip it. You can verify whether or not you installed it correctly by viewing the mods list which you can access through the game's main menu.
Dependencies
Many mods use Factorio's base mod as their only dependency which you do not have to install separately. However, some mods may require you to install other mods for them to work and can also make suggestions for you to install other mods for them to extend their functionality.
Required dependency
When a mod you installed requires you to install another mod for it to work, the other mod, in this case, is a required dependency.
Optional dependency
When a mod makes a suggestion to install another mod, but if it does not need that other mod for it to work, the other mod, in this case, is an optional dependency. You can install the optional dependencies which extend the functionality of a mod to enhance your gaming experience with the mod.
Sidenote
Currently, the in-game mod portal does not automatically download neither required nor optional dependencies; therefore, it is up to the user to find and install them. However, such process is expected to be made automatic in the future.