Step 1: Slime
Another Instructable slit the tube with a knife, inserted the Slime through the slit, and added a tire patch. The problem with that approach is that the least amount of Slime on the surface of the tube makes it impossible for a tire patch to stick. This Instructable will show you how to drop the valve core inside the tube and put it back in place after adding Slime to the tube. In the interest of disclosure, this basic procedure is described on the Slime website. I have illustrated it here with some things I learned by experience.
Slime coats the inside of your tire tube as your wheels roll. When there is a leak, the air moving through the leak draws some of the Slime into the hole and tiny shreds of rubber plug the hole. A tube with Slime added can last a very long time after a leak developed and sealed, even at pressures of 100 pounds per square inch.