Welcome to the wild and woolly world of 3D modelling. Heh. There are a couple of free programs out there that people use. I think Blender:
http://www.blender.org/ still might be the "best"?
I also don't know a thing about it, but Google Sketchup is supposed to be pretty slick, at least for more inorganic things:
http://sketchup.google.com/I think any free modelling program you'll find will have tutorials...somewhere. I'm sure Blender has some on their site. I don't have many tips to offer, as it's been a while since I learned myself and I haven't much used these programs: Start from primitive shapes, learn the tools, and bend them to your will. It does sort of depend, a little, on what you want to model.
Good luck!