1) First you need something to unzip:
Download and install this (Izarc Unpacker)Link
2) Download the mods
3) Double-click the .zip file -> this should open Izarc
4) Click on "Extract" or "Unzip" or "Extrahieren" (depends on the Izarc version) -> a small window pops up - click on "Extract"... again
5) Close Izarc -> now there's a folder named like the .zip-file in your directory where you downnloaded the mod
6) Read the readme (if there is one)
7) Copy the files (except .pcx, .mdl, .bik -files - see below) into your ...\galciv\Mods\Data Folder
(note that Invasion Tactics and Up-Issuses have their own folder in ...\galciv\Mods\Data)
AND/OR .pcx, .mdl, .bik -files into your ...\galciv\Mods\Gfx Folder
(note that Party Logos and Tactic Images have their own folder in Mods\Gfx).
Restrat GalCiv and start the next new game, the mods should be working now. Keep in mind that some mods will work only with the AP expansion (like maps).
I hope this helps a bit. If you have any further troubles, feel free to ask.