There are a lot of ways to deal with a sport anchor. Jullie Ellison at Climbing magazine hosts the following video where a very simple and relatively safe way to do this is discussed.
It should be noted that climbing is not "safe" and if a mistake is made in this system, the results could be catastrophic.
Steps to Cleaning a Sport Anchor:
1) Once you reach the anchor, clip two draws into the anchor. Ideally, the gates of the draws are facing away from one another.
2) Clip the rope through one draw and clip the second draw directly into the belay loop. The belayer should keep you on belay the whole time.
3) Pull slack between yourself and the draw that the rope is running through and then tie an overhand or an eight.
3) Clip the loop in the overhand or the eight to your harness with a locker. This will allow you to have redundancy while transitioning.
4) Untie the figure eight that is tied into your harness and run it through the chains.
5) Retye the figure eight into your harness. Double and triple check that this has been done the right way.
6) Remove locking carabiner and knot.
7) Test the system by weighting the knot on the belayer before unclipping yourself from the draw.
8) Clean the draws and then lower to the ground...
There are a lot of ways to do this. Some people lower from the anchor, while others rappel. It's important to tell your belayer while you're still on the ground what your plan is; and if you plan to lower, there is never any reason to ask the belayer to take you off belay. There are several accidents a year due to miscommunication surrounding anchor cleaning...
--Jason D. Martin