I think this is what you're looking for. Also the documentation has the basics for these operations. Check out the file and see if it makes sense. There are 3 layers in the file (points, wireframe, solid). All you're doing is going from a simple wireframe to a solid and the Solids menu is where you need to look.
Start with a 3d wireframe for the star. Then add surfaces to the wireframe by making triangular planes using Solids->Surface Creation->Planar Surface. Create the "base" with the same function. Just select the wire geometry and use the menu function. Then I used Solids->Stitching->Stitch Surfaces to Solids to make a single 3d object. That's it.
One trick with an object like this is to make one set of adjacent sides, then copy/paste them using rotate around 360 degrees and 5 copies. Also, I'm using V20, so your menus may vary.