We have our own 12-step program. It works great for the impossible 18x1 and 20x1-1/8 tube changes.
Take the entire tire off the rim
Trash the old tube
Run your fingers inside the tire checking for pokey things
Get the new tube and put some air in it to give it shape
Stuff the tube into the tire. You may need to deflate it a little.
Insert the valve stem into the hole
Work the tire back on the rim. One side is easy, the other side needs tire spoons (plastic kind)
Once the tire is on the rim push the valve stem up into the tire to make sure it is not caught in the bead
Work your way around the bead squishing the tire to check make sure the tube is not sticking out
Air your tire up to about 20psi looking for any odd spots in the bead where the tire did not seat
If you find a spot, deflate, adjust the bead, and air it up again
Air the tire to the desired operating pressure
You can leave one side of the tire on the rim and just work the tube in on open side. This doesn't work as well with the thin little tires on the small BMX race bikes though. Also, we take the tire off to check for bad spots or thorns because we live in an area with lots of pokey plants.