Okay let's see. Most campaigns will just be mission and campaign files but just in case here's a bit of a guide.
.fs2 - Freespace mission Freespace\data\missions
.fs2 - Freespace campaign Freespace\data\missions
.pof - Freespace Model file Freespace\data\models
Those 3 are easy. After that it gets a little trickier.
.tbl - Freespace Table file Freespace\data\tables
If the .tbl is over 200k in size you can probably just dump it in that directory. If it's only a few k in size beware as it isn`t a complete table file just a fragment you're meant to cut & paste into the real one. For details on how to do that click the link at the bottom of the page.
.pcx - Texture or interface art. If there was a .pof file with the mod or if it says that it was a skin mod stick it in \data\maps. If that doesn`t seem to work it could be that one of the files is meant to have gone in one of the other directories (\data\interface is a reasonable bet). Drop a line to the creator of the mod and complain that he didn`t include a .readme file telling you that.
.ani - Several places this should go depending on what it does. There REALLY should be a readme to go with files like this. Freespace/data/interface is a good bet if it's a ship's icon.
.vp - Volition Package file. Similar to a zip file in that it's a single file which contains lots of files inside. You don`t need to extract it though. Just stick it in the freespace directory and you should be okay.