I have done about five of them, and only broke one. Do this: do whatever you gotta do to get the old tire off, I used the rounded edge of a crescent wrench. Get two of them and put them about 3" apart on the tire, and pry the tire over the lip. Once it's started, it will go really easy. Then just use a whole bunch of car wash soap on the lip of the rim and work one edge of the new tire on. You will have to pry it on their. Push the tube inside the tire, and work the stem through. Inflate the tube just a little bit and feel around with your fingers to make sure everything's away from the lip. Put car wash soap on the lip of the rim again and use your knees and palms to get the tire almost on, then use that crescent wrench again to pop it completely on. Fill it up and bounce it around the tire to get the bead to seat properly, and your good.
It's easier to show you. Where are you located? I'm in Omaha, but there's probably someone near you who wouldn't mind showing you the first time.