On the left and right side of the head unit there are small plastic strips. Take a screwdriver and wrap the head in tape, then gently pop them out by taking a tape wrapped tip and put it between the head unit and the surrounding bezel. After these are removed set them a side, under these smalls trips will be several holes. The holes that you will be dealing with are the two largest holes on each side. From here you can go buy a tool to remove the head unit, it is called a Ford/Mazda stereo removal tool. or you can fabricate a similar tool out of a hanger. The tool is only five dollars and it will make the removal infinitely easier. The tool looks like a pice of wire shaped like a U with the diameter about an inch and a half. Take one end of the U and put it in the top hole and the other in the bottom hole, do the same on both sids. After the U is inside the head unit you will then push them in about an inch and a half. from there you are going to pull the loops of the U together. This action will depress a small spring inside the head unit on both sides and allow the unit to slide forward. If you use the tool it will engage the spring very quickly and will stay in place, the coat hangar will not say in the same place and will require much more finesse to get the unit to come out. You must pull both sides out at the same speed because the unit will not fit out of the hole if you pull at an angle. When you get the unit out there will be three plugs in the back if you have a tape deck or CD carousel, and only two if it is only the head unit. Unplug all of the plugs, two of them are standard computer style multi pin connectors and the last one is a long pin for the antenna. After all of these steps are finished the radio will be removed. If you want to remove the tape deck the process is the same only you will have to unplug only one connector in the back.
Have fun and Good luck, I have removed almost every part of my 1999 Miata and put it back with out a service manual and the car is running great at 120,000 miles. You can do it.