Begin hardening off your seedlings about a week before their transplant date. (Check the seed packet for the estimated date in your area; it varies depending on the variety of plant.) Keep the seedlings well watered throughout the process.
Set the containers (whether flats or individual pots) in a sheltered, shady spot outdoors. A covered porch is an ideal starter spot, so is a table or bench under a leafy tree. Bring the plants back inside at night, and bring them in at any time of day if the weather turns cold, windy or rainy.
Expose the plants gradually to more sun. After two or three days, you can safely keep them in the sun for half a day, then return them to the shade. By the end of the week they'll be tough enough to soak up the rays all day.
Transplant the seedlings to the garden on an overcast day to ease the shock of transition from pot to ground. If a light mist is falling, so much the better.