Under the Apple menu, select "About This Mac...", then click "More Info..."
this will launch System Profiler. Unfortunately the common model name (e.g. something like "A1054" for an Early 2004 iBook) will not be listed by System Profiler, but other useful and uniquely identifying info will be shown there.
you can then cross reference that info in the handy app called Mactracker. knowing a few pieces of info about your machine, e.g. the processor speed and general model type(e.g. iBook) will usually lead you to the specific model. There's also a unique machine identifier shown by System Profiler (e.g. "Powerbook6,5") which can be searched for in Mactracker to give you the more commonly known model name