(note: if you're a mod maker, I'd recommend that you don't do it this way; use a mod script. If you really want to, though, you can, and the auto-installing mod archive (*.zip.flmod) also works with this way)

First, install and run FLMM v0.6 (or higher). Then, go to "Tools/Open mods folder". Create a new folder there, titled the name of the mod. Then, extract all the files for the mod into that folder, making sure the files are in their right subfolders. For example:

Program Files\Freelancer Mod Manager\mods\SomeMod\data\equipment\market_misc.ini
Program Files\Freelancer Mod Manager\mods\SomeMod\data\ships\shiparch.ini

You can also add a scrip.xml file into the SomeMod directory that contains just the header tag, if you want author & description info.

Any questions? Let me know!