How do you loosen the tension on an alternator so that you can put a belt on it?

Usually you can loosen the tension on the belt by moving the alternator. To do this, you need to loosen the bolts securing the alternator. It usually only has two, a pivot bolt and another bolt that slides along a track. You don't need to completely remove either bolt. Simply loosen the both of them, and the alternator will pivot towards the inside of the belt, allowing you to take it off. Put the new belt on pull the alternator towards the outside of the belt until it is tight, tighten the slider bolt, and then tighten the pivot bolt, and you're all set!

If the vehicle has one belt for everything (serpentine belt). This vehicle more than likely has a center tension pulley with a bolt or nut on the front. Place a boxed wrench on this and try tightening it. It will more than likely move releasing the tension on the belt where it can be entirely removed. It will be spring loaded so you will have to hold with one hand and remove with the other. Most vehicles also usually have a belt route sticker which will help if you forget just how it was routed.