My 2006 grand touring mazda6's ac is not working, my relay is working and ive filled it with coolant recharge, my ac pulley is turning on the outside ring,(because of serpentine belt) but the inside which i think is the compressor part wont turn at all. I need to now if theres something else i can check or if i have to get a new one, and if so what is the best way to get to it to replace it myself?

SOURCE: replace AC compressor clutch

you will need to have the small tool kit that comes with both tools for pulling and installing clutch assembly. Check with Autozone and see if they have it in their tool loan program.

SOURCE: NEED TO ROUTE SERPENTINE BELT AROUND SEIZED AC PULLEY ON 2001 TAU

Some Parts Stores Have A/C Bypas Belts you should call around

SOURCE: serpentine belt slips off idler pulley

The A/C pully is supposed to spin freely until the AC is activated to run.. The cranshaft pully does not. Replace the tensioner pully. The belt has to fit in between the grooves on the pullys.

SOURCE: i NEED 2005 mazda6 Serpentine Belt Routing

There are 2 engines for your Mazda 6, a 2.3 and a 3.0. Below are both diagrams:
2.3


3.0

SOURCE: A/C compressor pulley is seized and burning the serpentine belt

yeah its seized up[ and they dont make a repair kit for that one either. they have at most auto parts stores an ac bypass pulley . its a bracket and pulley so you can bypass the factory ac unit and still run the factory belt. but if you decide to change the ac unit there are 5 bolts holding the unit down .have the system evacuated.loosen belt and drop down out of your way. take the ac lines off the compressor and set aside . there are two bolts on top in front and there are 3 bolts in back on top tieing together a triangle shape mounting plate , take all 5 loose and out.disconnect ac wires (snap clip) lift , lightly pry off old ac unit.set aside and reverse the procedure to install your new or salvage yard ac unit. refrigerant chargers can be purchased from wall mart ( there cheaper) at $30. roughly 2 1/2 cans will completely fill the system just follow on label instructions. its all easy to do if you can use wrenches and have a little knowledge. and you get the satisfaction of doing it yourself. and save a bunch of $ along the way.