Just select them in the PSS menu. There are different ones that do different things, like give you more experience or more prize money, or make Pokemon easier to catch. This affect lasts for a short duration (I think it's 3 minutes). When you get the O Powers from Mr. Bonding they will be at level 1. When you use an O Power a lot it will eentually upgrade. I don't know how many times one can upgrade, but upgraded O Powers give better benefits than lower ranked ones (e.g. more experience or whatever).
After using an O Power there is a cool down period, so you can't just keep activating it every 3 minutes or whatever. You can use them on yourself, or you can use them on Friends/Acquaintances/Passers-by. If you use them on friends (etc.) then the cool down time is a lot less (but you obviously don't get the benefit from it - your friend does). This still counts towards them getting upgraded, though.
I hope that made some sense to you. Really, the best way to work it out is go and have a play with it yourself.
