I did Give Kids The World once and it was very fun and I wish I had gotten to do it again, but I always worked on those nights. they gave us a sheet at check in with info about volunteering there. the housing programs office sends CP there every wendsday and sunday night to help with activities. you call the programs office a week before to sign up, but they only take so many people each week, so if there is space you can go. they provide transportation there and back.
VoluntEARS is through the whole company, i believe they have their own website where you can register and look for events to volunteer at and sign up. If you don't have a car it may be hard to get to some of the places.
I know some of my managers at work would also tell us about events sometimes too. I think some things were on property and would have been easier to get to. If you talked to a manager i'm sure they could get you info or point you in the right direction.
My roommate and I volunteered at a playground build at a boys and girls club. It was very hot, but lots of fun. there were a ton of Disney VoluntEARS there and Handy Manny was there as well!