The first is the ProGrabit Screw and Bolt Remover. I use this piece when I have stripped the head of a phillips head screw. This 3 piece kit contains everything you need to remove screws (sizes 4 thru 14) and small bolts.
To use it you, place the appropriate sized extraction tool in you drill in and run it in reverse to create a cavity in the screw or bolt head. You then flip the extraction tool in your drill so that the screw end can be inserted into the cavity. Again, running the drill in reverse, you back-out the screw or bolt.
The second option is the Cut-around Screw Extractor. I use this when I have snapped the screw head off of the screw completely.
You simply chuck this miniature hole saw into your drill, center it over your broken screw, then cut a plug out of the wood with the embedded broken screw in it.
When finished, you have a nice clean hole where your mistake once was. You can then plug the hole with standard size dowels or plugs cut with a tapered plug cutter. Cutting your own plugs will allow you to match the wood type, color and grain closely if you have some scraps from which to cut the plugs.