Mods come in a special zip format, flmod in fact (so its filename.zip.flmod)
To use them, you need a cunning application called "Freelancer Mod Manager" - or FLMM for short. Once you download and install FLMM, you can then simply download (either opening from location, or saving to your hdd and then double clicking) any mod, and it will unzip itself into flmm's directory. When you start flmm - you will then see the mods name in the window, which you can either double click on to activate, or click on to select - then click on the green arrow to activate.
To deactivate, select the mod that is deactivated, and then click on the red cross to deactivate (or double click the mod once more instead).

FLMM is in the downloads seection, if you click on the number of downloads - it will sort them into numerical order. FLMM should be the most downloaded mod, with around 100,000 downloads or so.