Make a folder in your twilight folder called 'mods', without quotes. Create a folder in mods for the ships; let's pretend it's 'NewShipMod'. Create a folder called 'Data' in that NewShipMod. Create the folders 'ships' and 'shiptemplates' inside Data. Look inside your downloaded .zip and put the files where they go in these folders. I hope for your sake the ship author has preserved the folder structure in his .zip instead of having all the files jumbled in one big list.
Now, you'll need an .xml file in 'NewShipMod'. This is for the in game description and is necessary for the ship mod to show up in GalCiv. It may or may not be supplied with the mod; if it is not, go to your original Galciv folder, not the twilight folder, and look inside the folder called mods there. There should be an example mod, with an example .xml file; steal that one for your ship mod by copying it over into 'NewShipMod'.
Load up Twilight, go to Options, find the options for mods and load the mod. If everything is right the ships will be available for the specified race when you play.
I do not know if there are better ways to do this, but this is a way to do it. Copying the files into your documents\My Games\ twilight folder has not worked.