What you're talking about (blending three shots with different exposure settings) is called HDR (high dynamic range) photography. You don't need a camera which can shoot RAW in order to do HDR work (shooting in JPG is fine), neither do you need Photoshop.
All you'll need is a camera which allows you to, at the very least, change the exposure value (marked as EV+/- on some point and shoot cameras), and a tripod. A camera which allows you to change the aperture, shutter speed, etc is more flexible and therefore preferred, but a tripod is absolutely necessary as you can't always find a solid, stable platform to rest your camera on and you need to get three shots at least of the same scene exactly.
Photoshop is nice but there are plenty of other programs out there which will do HDR specifically and don't cost the earth. Photomatix is one such program but there are many others.
I'm not going to go into detail about how HDR is done as, generally speaking, I really don't like it and I don't do any myself. There are plenty of tutorials out there which will give you a good grounding in the technique though. Have a Google around for HDR photography and you'll find plenty of stuff to read.
Hope this helps!
George.