Pioneer DEH-P3300 and 94 Mazda
It's good that you have an aftermarket Mazda wiring harness. It will allow you to make all of the connections in a well-lighted and comfortable location rather than fumbling around behind the dash.
If you are somewhat skilled at soldering, the most secure, electrically conductive, and positively insulated splices are made with solder and heat-shrink tubing. You can get the needed equipment from any Radio Shack, Lowe's or even WalMart. Be sure to put the heat-shrink tubing on the wires BEFORE you solder them together. I had to say that! Because I've forgotten many times! But if the soldering route is not for you, get properly sized insulated inline crimp splices and the appropriate crimping tool. Match up each wire by function on the Pioneer harness with the corresponding wire on your aftermarket harness. Most of the time, the wires will be color-for-color matched. But make sure, sometimes wires for things like "illumination", "dimmer", "mute", etc may not be the same colors.
Disconnect the negative battery terminal while you are working behind the dash. After you have the harnesses spliced together, plug the radio end into your Pioneer, remove the old radio from the dash opening, unplug the antenna and wiring harness plug and plug the other end of your spliced harnesses into the vehicle plug and the antenna plug into your Pioneer's antenna connector. Slide the Pioneer loosely into the opening, but don't secure it yet. Reconnect the negative battery cable and test the receiver. If everything works, slide it into the dash opening and secure it. Use the rear support stud and rubber bumper if needed. Install the trim ring or separately purchased dash kit as required. Put the "face-fixing" screws in to prevent removal of the faceplate if desired. Reinstall any dash trim removed and you're finished.
Hope this helps.