There are almost as many methods around for doing this as there are researchers. And everyone swears by his or her favorite method. The fact is that probably all methods work to some degree, and most work reasonably well. For purification of PCR fragments, the more recent advances in this methodology avoid running gels at all, and of course, high throughput systems are becoming more common every day.
Fluorescent image is represented in a pseudo color scale.
Electroelution can be done simply by dropping the gel slice into dialysis tubing with a little buffer and placing it back in the electrophoresis apparatus. Alternatively, devices both simple and complex can be used for this. On the simple end are GeneCapsules, invented and sold by GenoTechnology and offered by Stratagene as Quik-Pic Electroelution Capsules. Gel slices are put into these chambers and, as with dialysis membranes, returned to the electrophoresis chamber for a few minutes to move the DNA out of the gel into the surrounding solution. When working with lots of samples, or if you're just plain tired of fiddling with dialysis tubing or membranes, you might want to consider one of the reagents or kits that can be used to extract DNA from gel slices.