Trouble with a converted STL file?

I recently took an STL file and imported it into SolidWorks, and I aimed to smooth it out and fix some details--it's made of a lot of polygons right now, and I don't intend to leave it like that.

I've tried several things, but I can't seem to make it anything other than a surface body, and I can't seem to give it thickness or smooth out the areas in which I need curves. Anyone have some suggestions? (Aside from remaking the part from scratch)

SolidworksParts And Features