Look at your installed files, you will find a subfolder unter your Mount&Blade path called "Modules". There you will find a folder called "Native". This actually is the regular modul you usually start.
Install the files of the mod (unzip/unrar whatever) into a new folder unter "Modules", many mods are already packed that way, like the "Sword of Damocles - Invasion" mod creates a folder called "Sword of Damocles - Invasion".
When you start Mount&Blade you can select a mod to play, the one you see at the start is always the last you played, currently "Native". The names you will see here are the names of the folders.
This applies to "full" mods that come complete with all files. If you want to install a modification of the "Native" mod I would advise to make a copy of the Native folder and copy the files there (hopefully these come with instructions...) so if anything happens you don't need to install everything again.
If you want to use old savegames (depending on the mod) you can also copy or rename your savegame folder.