I volunteered at a large shelter here in Pittsburgh. Mostly what I did was dog walking and some light training/socializing, and I also did some work with the kitties (just socializing, cleaning their cages, taking them in to adoption rooms to play and stretch their legs for a bit, that kind of thing). It was a professionally staffed shelter, so all the kennel-cleaning, feeding, and adopting was done by staff. Some smaller shelters are primarily volunteer-run so in those places I'd think as a volunteer you should expect more "grunt work"--scooping poop and doing paperwork and the like.
One word of warning from my personal experience: shelter volunteering can be mentally and physically exhausting. A lot of volunteers would sign up at the shelter thinking that working with the shelter dogs would be like petting cute puppies and walking a dog just like walking Fido at home. They'd stop volunteering pretty quick when they realized that walking an un-trained under-socialized adolescent pit bull is hard work. Its extremely rewarding and something I think every dog-owner should experience doing for a little while (just to see the other side), but it is often not very easy, just from a physical standpoint, let alone the emotional angle, which can also be tough.
I hope that helps a little. Every shelter has their own system for processing volunteers, and some make you take classes before you can begin (I had to take one class for the cats, two for the dogs, and have a certain number of hours of mentoring from a more senior volunteer).