Unfortunately modding FreeSpace is not a simple task. If you're serious about modding, you might want to refer to the
FS Wiki Modding Portal. Installing an existing mod basically consists of three steps:
1) Create a mod folder, and put the modded files in the relevant folders. Any packages (.VP) go in the root directory, textures (.PCX or .DDS) go into data/maps, models (.POF) go into data/models, and tables (.TBL, .TBM) go into data/tables.
2) Enable the modded ship in missions. This can be as simple as editing an existing mission (.FS2) in FRED or even Notepad, or as complex as creating a new mission or campaign using the new mod.
3) Launch FreeSpace with the mod enabled. You can do this from the 'Select Mod' button on the launcher. If you have all the files where they belong, and there's no conflicts, you should be able to play with it.
Most mods on FreeSpaceMods.net are designed to be used by mission designers for use in complete campaigns, and it's difficult to just plug in a new ship and expect it to be available in the main campaign. Add to that that everyone who uploads to FreeSpaceMods.net uses a different packaging and release system and you'll quickly have a mess on your hands.
Unless you're really enthusiastic, you might want to download and play completed campaigns that use new mods, such as the FreeSpace Upgrade Project Media VPs, FreeSpace Port, Blue Planet, Procyon Insurgency, or Inferno.