Kevin, Mitch, and Bill have pretty well covered just what I was going to say. Be sure to use a powder, such as talc on the tube. I bought some body powder at K Mart that works well on inner tubes. I sprinkly it on fairly heavy and rub it to completly cover the tube. This is important not just for mounting, but so the tube doesn't stick to the tire from age and heat. I removed an old inner tube once that was just as though someone had glued it to the tire. I inflate the tube to about 2/3rds full, install it and then install the other tire bead. I just did 4 inner tubes on two lawn tractors and used Vaseline on the tire beads to help them slip over the rim. I then bounce the tire as I turn it around to help settle the tube. Then as Bill said, inflate it without the core, just enough to push the tire to it's position on the rim. I then let the air back out of the tube, and shake it a little to make sure the tube is in the correct position. Then I insert the core and inflate to 32 pounds pressure. BTW, the instruction sheet that came with my inner tubes said to start the tire bead on the side opposite the valve stem, and finish installing the tire at the stem.
As carefull as I was trying to be I used a screwdriver on the 12" tire and poked a small hole in the new tube. Nothing worse than having to patch a brand new tube.
The Carlise tubes are much better than the ones at Fleet Farm.
On Model A 21" wheels I will use a tire tool to start the removal of the tire, but I've always been able to install tubes and tires without any tools.