I have found that one of the main reasons that new transplants wither and die is due to inadequate hardening off. If you start the plants indoors under lights, or in a sunny window, don't forget to provide a fan, to make the stems sturdy and strong. Otherwise, when they are put out in the garden, the spring winds will just dry them out and make them wither and die. Even with using the fan, they still need to be slowly introduced to the sun. I use an old work table placed near the house, where I can control the amount of sun they get. You need to study the sun shine on your selected area, and start off with maybe a half hour of sun, on well watered plants. Gradually increase the amount of sun over a 10 day to 2 week period. When not in the sun, the plants can be outside in a shady, mostly protected spot. Then when you do set the plants in the garden, protect them from the sun and wind for a few days, like Digit'S said. It takes some dedication, but worth it.