Pry one side of the tire off the rim all the way around with a tire lever designed for that purpose. Don't use a screwdriver as it may nick the tube. Reinsert the stem, and lightly pump up the tube....make sure it is evenly placed around the rim. Deflate the tube again, and push the tire in the rim with your thumbs or fingers. Push the stem in a bit to make sure the reinforced section of the tube is inside the tire bead. Then pull the stem out and inflate. As someone said, you can press your thumb against the outside of the tire above the stem to make sure you don't push it in again.

One other point. Inside the rim is a rubber strip called rim tape that protects the tube from the spoke nipples. Make sure the stem goes through the hole in the rim tape. Sometimes it's a bit tricky to get that in.