Any recommendations as to the best way to see the island of Burano near Venice? We are travelers who prefer not be part of a tour group. Is there an affordable way to get to the island without having to go with a tour group? If so, how? What places are a "must see" on Burano?

There's no need to visit Burano as part of a tour group. Just take a vaporetto from Fondamenta Nuove to Burano. Theisland is samll and easily explored on your own. If you have time take the ferry from Burano to Torcello, only about 10 minutes away.

Maryk is totally right. Burano is tiny and you can visit along with Murano and Torcello, which are very small as well.

if you have a vaparetto pass, it is free to go to and from burano.

You can easily do on your own. Consider making your way across Venice to Ponta de Nove (I think? I'll try to look it up for you) it's closer to Burano, it's a shorter ride, and many more vaporetti go from there than from San Zacharia. But if you don't want to do that, you can easily take a vaporetto (check and make sure it goes in the right direction for you) from the San Zacharia stop -- I think there's a 10:15 a.m. waterbus (of course check the schedule). Once on Burano you'll see that it's pretty easy to find your way around.

I agree with the other posters that Torcello is well worth a visit, and so close by. If the budget allows try to eat at Locanda Cirpriani.

We visited Murano, Burano and Torcello in one day. We used our vaporetto pass for the passages. Can easily be done on your own. The islands are small, and easy to explore.