There is really little movement as I stabilize the bike with one hand. What I use to remove the tire depends on the individual tire. Some are loose enough that I can do it with just a finger. If not a Speedstick works well or I keep a set of plastic tire levers in the seat tube of each bike. They weigh just ounces and are handy. I also keep a micro-tool in the bikes I ride the most.

I recommend practicing this at home to get an idea of what you are doing. Once you have it down it goes really quickly. I also found that it is easy to repair the old tube this way and then re-use it later. Of course you could Slime the tire but I am not really in favor of that as you can still get flats and it adds a lot of weight (much more than a tube) and it slows you down quite a bit. So do tire liners for that matter and tires like the Marathon Plus. I’ll take my chances with the normal tires and carry a spare tube. Of course if I was in a very flat prone area I would still do what I do with the spare tube but go with a very flat resistant tire like the Marathon Plus.