Set the peat pots holding the sunflower seedlings in a shallow tray. Place the tray outside in an area that receives bright light but is protected from direct sunlight and wind. Set the tray outside only after frost danger has passed.
Leave the tray outside for four hours the first day, then bring the flowers back indoors. Gradually increase the time the transplants spend outside each day over the course of a week until the plants spend an entire day outside and become accustomed to outdoor conditions. Gradually increase the seedlings' exposure to direct sun and wind as you increase the length of time spent outside.
Turn a 1-inch layer of compost into a well-drained, full-sun garden bed using a shovel. Compost provides nutrients and improves the soil quality in the planting location.
Dig a planting hole for each sunflower transplant. Make the holes the same depth as the peat pot but twice as wide. Spacing of the holes depends on the sunflower variety. Space standard varieties 1 to 2 feet apart and giant types 3 feet apart.
Tear the rim off each peat pot so the rim of the pot is even with the soil inside. Set the pot into the planting hole so the rim sits level with the surrounding soil in the bed.
Fill in the hole around the pot with soil. Cover the rim of the pot with a thin layer of soil. If the rim protrudes above the soil, the peat pot will wick moisture away from the sunflower transplant. Water the bed thoroughly after transplanting.