you should be able to remove the bazel by prying a little bit. be sure to remove the screws under the dash. after the bazel is off the rest is easy.
Also determine the kind of radio you want to put in. What is the size? Is it din, din and ½, or double din. With a mazda my guess is it is din, which is a pretty standard size so you can get just about any OEM player/radio around. Then get an automotive wiring book to help you with the wiring. I have a few web pages that describe my various exploits: