This was really cool. You can get a guide to Kizmkazi in Stone Town or on the north end of Zanzibar which includes round-trip bus travel and boat rental. You probably will have to share with about 10 other people. They have some gear available that's sufficient for the experience.
We swam with a pod of about 15 to 20 dolphins for about 2 hours. It was awesome to say the least. They cruise pretty fast but you can keep up with them if you push yourself. Every so often they would suddendly change course and you would end up in the middle of them, some of the dolphins only a couple of feet away. If they are moving too fast or you can't keep up, the boat does a decent job of leap-frogging their course. Just climb back in and get dropped off in front of them again.
I've been on a lot of dives around the world (both snorkeling and scuba) and this was one of the funnest experiences I have had. I swam full speed for about two hours and hardly even noticed. I highly recommend this activity if you are on Zanzibar.