Cleaning an anchor is actually pretty simple. It is also pretty safe if you have a plan. The main thing once again is to communicate with your belayer. Let them know if you are expecting to get lowered or you are going to fix a rappel and rap off on your own. There is no right or wrong choice between these two, it all depends on the situation..
If you are just starting out try your chosen method in a safe secure environment. Your climbing gym and/or your local crag if they have a teaching area set up. Once you think you have the system wired and a plan your most likely good for life. Climbing sport is actually very safe. The only thing is you have to do a few critical things well. Building an anchor, belaying, and cleaning an anchor are a few of the key ones.
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