There are two different motors in a Mazda 3 which take two very different oil filters with two very different procedures in how to change them. In the 2.0 litre engine, the Mazda 3 has a conventional canister oil filter. In the 2.3 litre, however, the oil filter is a cartridge filter that will need some speciality tools in order to replace. Save the money on labour charges on oil changes and invest in the tools if you have the 2.3 litre model.
Park the Mazda 3 on a flat paved surface, release the hood latch, and apply the parking brake. Place a wheel chock behind one of the rear tires. Open the bonnet and remove the oil fill cap.
Lift the front axle of the Mazda 3 one side at a time with the floor jack and place the jack stands under each left and right control arm.
Put on the safety glasses and crawl under the front of the Mazda 3 on a creeper if you have one. Remove the splash guard covering the oil pan and filter with the ratchet and a 10 millimetre socket. There are 7 nuts and two fasteners. Turn the fasteners counterclockwise.
Remove the drain plug from the oil pan (since most likely you're changing the oil or why else would you want to remove the filter?) with the ratchet and 17 millimetre socket and allow to drain into the drain bucket.
Remove the canister oil filter using a standard oil filter wrench by turning it counterclockwise. Be sure to remove the rubber gasket of the old filter from the oil filter flange on the motor if it sticks to it. Add a light coating of spent oil to the gasket of the new oil filter and screw onto the threads of the oil filter flange hand tight. Replace the oil pan plug, splash shield, fill the car with oil, remove the wheel chock, and lower the vehicle.
Follow steps one through four in the 2.0 litre version.
Remove the centre plug of the oil filter cover using the 6 millimetre Allen wrench key and allow it to drain thoroughly. Replace the gasket on the plug. (supplied with new cartridge oil filter) Replace the plug and tighten when the oil has drained.
Remove the oil filter cover using the oil filter ratchet wrench, the 3 inch long extension, and a ratchet, turning counterclockwise.
Remove cartridge filter and replace the oil filter cover gasket (supplied with new cartridge filter). Insert the new filter into the over until it clicks/locks into place. Tighten the oil filter cover thoroughly.
Replace the oil pan plug, splash shield, fill the car with oil, remove the wheel chock, and lower the vehicle.