If you volunteer, you are accepting whatever the airline offers. Meaning, they could just ask pretty please and if you volunteer, you just get the personal satisfaction of helping out the Gate Agent.
However, airlines tend to open these days with a few hundred Dollars/Pounds/Euros in travel vouchers to entice enough people to volunteer to prevent bumping. If you volunteer for a next day flight, you should also get accommodations if not at your domicile.
From experience, I'd expect 200-300 as a start.
Also, there are many strategies to maximizing the payout. It's a balance between holding out for the maximum compensation and getting on the list before they don't need more volunteers. Knowing when the next flight is really helps. There have been many times when I've volunteered quickly because I know the next flight is maybe 2hrs later.