google sketch-up?

depends on what you plan on using sketchup for. just a simple model with very little detail could take the beginner a while, but for something complex that program has a lot of tricks and commands that can be quite frustrating (plus you only get a limited number of hours for free).
never heard of any public domain CAD software because most if not every CAD version i've used is copyrighted. if you're looking for a cheap version you might try AutoCAD LT (light), same basic functions of CAD. unless you're looking to build terrains, 3d models, etc.