One of the hardest parts while rappelling is often the top edge or lip, especially if the lip is underhung or the anchor is low to the ground. Here are a couple of techniques that people use when getting over the edge.
Soft Start
This method is hard on clothing but usually doesn't pinch fingers or cause people to flip upside-down. It also doesn't put a large force on the rappel anchor, which is especially useful when using marginal anchors like deadman anchors, sandtraps, or similar.
Static Edge Negotiation
This method is great because it's slow and controlled and doesn't take a huge amount of coordination.
However, if you don't lean far enough back and you step down from the lip too soon, you can swing into the rock and pinch your left hand between the device and the rock or you can smash your face into the rock.
If you lean too far backward, you can flip upside-down, which scares people but doesn't do any damage unless you happen to pinch your foot under the rappel rope, which I've seen happen multiple times. It can be kind of hard to release your trapped foot.
Dynamic Edge Negotiation
This method is very fast and smooth but requires some coordination and a good feel for your rappel device and how much rope to let out how quickly.