How to elute a protein band of interest from SDS-PAGE or Native-PAGE gel?

If you are interested in trying to recover functional protein (as suggested by your interest in Native-PAGE), then you are far better off not using an SDS gel in the first place. Bio-Rad makes an apparatus specifically for running native tube gels and these are actually easier to recover protein from than slabs.

The process involves sectioning the tube gel with a purpose-built device that holds multiple razor blades that can be spaced in increments of 1 mm from each other, allowing up to about 100 slices from a 10 cm gel. However, in practice, slices are ussually cut at 2-3 mm thickness to avoid crushing the gel during cutting and for ease of handling. The recovered slices are then individually crushed and eluted as Matteo describes above, and activity assays can then be run on the extracts (this process can also be done with slabs, but it is a little more troublesome because you need to isolate the individual lanes before sectioning them).

If, on the other hand, you have to use SDS-Page for some reason, and you are trying to recover functional protein, you will need to visualize and recover your band, and then remove the SDS and renature your protein (typically SDS is removed by acetone precipitation and the recoved protein is usually renatured in a 6M Guanidine-HCl solution - there are numersous protocols in the literature.).

If, on the other hand you are simply interested in recovering isolated protein for sequence analysis, you should blot it to PVDF, stain, and cut the band of interest from the blot with a razor or scalple. More specifically, you could cut the band from the gel and put it in an eppendorf with few microliters of the loading buffer for eletrophoresis (or another buffer suitable for your next step). You can then chop the piece of gel up, vortex it and also let it in contact with the buffer for a while (sonication helps as well) so that the protein band can pass into the buffer. After that just spin the gel down and recover the buffer with your protein. You can than concentrate it, dialyse it or reload it directly on another gel if you want to run it again.