Need help on how to wire a REAR fog for 2006 Mazda 3 S
 

I need help on how to wire my REAR fog lights using a Mazda protege fog light switch. All my wirings are layed out already all I need to do is wire it to the battery or a relay to make it light up using the Mazda Protege switch. Thanks.

One more thing, What are the 4 wires from the Mazda protege for? Which wire goes where? plus the 21 watt bulb of my rear fog lens has to wires. What is it for is one a posotive and the other is for a negative one?

ok, well it's a month old post, maybe you finished this by now...
First off, you will need a multimeter... the outside case of the bulb is generally negative and the tip is positive. If there is any metal on the light housing, test to see if it is connected to either terminal of the lamp - if so that needs to be the negative, but likely it's isolated.
Wiring the lamps, tie the negative to the frame, I know there's a ground lug on the passenger side C-pillar that you need to take the trim off to get at, there may be another on the drivers side. Or you can find a bolt anywhere in the trunk, like what's bolting the trunk lid in place.
The positive should be passing from the battery, through a fuse, through the relay contacts, and then to the rear fog lamp.
The light switch wiring should have 2 for an indicator light (12V for night illumination) and 2 wires for the switch contact. This can also be found by using a multimeter, or by eye, I can see the lamp and PCboard are visible in the pics you posted.
The light switch needs to feed power to the relay coil, most relays are not polarized, so you can attach either wire as positive and the other to ground. Relays are typically wired with a hard connection to positive (you can use the + voltage fused that goes to the battery from the relay contacts) and then attach the switch in line with the other coil contact to ground.
I think this is everything, but if you need further assistance just reply and I can draw up a schematic or something.
Good luck.