Rivendell Bicycle Works has made some excellent how-to videos, such as this one:
How to Mount a Tire Caution: if you don't like Bob Dylan's music, hit "MUTE" now.The rest of Riv's vids are HERE. I love their production style - the antithesis of slick. I also like to take the tire completely off the wheel when fixing a flat, but other some people like to take off just one side, and pull the tube out. Both ways work fine. There is no single correct way, just as there is no single incorrect way.