?? Remove the alternator, they usually have 2 bolts holding them in place, slide the accessory belt off the pulley, don't forget to disconnect the pin connector (if equipped) and the positive cable. Replace with new (reman I suppose) alternator. Take up the slack on the accessory belt by using the mounting bolts/eccentric cut-out on the bracket to tighten the belt, some systems tighten using the threads on an adjuster bolt vs. pulling back on the alternator and tightening the mounting bolts, I don't know which this model has since I never worked on a Mazda5 in the past, but have worked on my fair share of cars/trucks including Freightliners.
Run the car for a few mins, shut off, go back and check the tension on the belt, after running the engine you will have to re-tighten the belt, you can also get fancy and use a belt tension gauge but this isn't NASA's jet propulsion labs so just use your hand to push down on an area between two pulleys, it should not feel rock hard that you can't move it, but should not feel flappy, should feel in between.
That's pretty much it. Oh yeah, your "supposed' to disconnect the battery, that might help so you don't short it out if the positive alternator cable touches the chassis. (drinks)
