Step One: Extracting the Model
The first thing we need to do is extract the models from the homeworld.big file. This is a pretty easy step. Download and open the BigViewer program. There will be a button that says "Load Big File." Click on that and browse to your Homeworld directory. Open homeworld.big and watch it load and process all 13851 files in the file. Once it's done we can see there are a whole slew of files in there. But only some of them are the ships we want.
The folders we want are derelicts, p1, p2, p3, r1, r2, and traders. Find the folder, highlight is and then select "Save Files (Recursive)" in the File menu. This will save the whole directory. The other folders have a bunch of other stuff that we don't need.
Well, that was easy. Now, if you go into your Homeworld directory, you will see a few extra folders. Pretty cool. Don't worry about messing up any of the files in there. If you screw one up, you can always re-extract it from the .big file. Pretty slick, huh?