It depends on the airline (in the US at least) as to what the offer is, it could be something as simple as a free ticket, US air offers combination tickets, where it could be used as a free ticket or a dollars off voucher on any flight (so you can apply it to part of a trip to eurpoe for example). There may or may not be cash included in the offer. It really depends on how bad they need the seats.

How to make the most of it?

Pick flights where you are guaranteed to be bumped. Once you figure out how to do that, sell the concept here and make a million dollars.

Probably the easiest way is to always ask at the gate as soon as you get there, are they looking for volunteers? Try to use only carry on bags, some airlines will pick somebody with no checked luggage way before somebody who checked bags, as they have to pull the bags from the planes.

Be flexible in your plans, and expect to volunteer way more then you are actually used, and expect if the flight they are putting you on is full, you may have a middle seat.

If you are sitting on a regional plane, and the gate people come on and say something like

"Pardon us folks, we have a situtation where we need"

Don't let them get past the wood volunteers without jumping at the offer, as you may be sitting next to me and I'll snag it.