If you have a very sunny garden, consider yourself lucky. Yours is the spot every gardener with an overhanging walnut tree or a north-facing yard dreams about. Plants need sun to grow, and in most cases, the more, the better. However, in hot climates--particularly in the Deep South--sun can actually be a bit of a problem. There are a variety of strategies for dealing with this though, so count your blessings and start planting.
Search out sun-loving seed varieties. Choose plants from hot or arid climates that will do especially well--melons, cucumbers, squashes, peppers, eggplant, tomatoes and herbs, in particular.
Water the soil thoroughly over the whole bed to cool it before planting seeds and to provide the dampness seeds need to germinate properly.
Dig furrows with a hoe to the recommended depth on the seed package and sow as directed; cover and tamp down firmly. Keep soil damp until seedlings emerge.
Improvise a sun blocker on the south side of each seedling until it is mature enough to tolerate full sun for most of the day. A wood shingle or piece of cardboard leaned against a stick in front of the plant will do, or you can make substantial shade for entire beds. Use lightweight frames of PVC pipe, saplings or bamboo. Fasten together like tables without solid tops, or make a simple "A"-frame; drape shade cloth or old sheets across these, or place leafy branches across for dappled shade.
Give adequate water to seedlings as needed--often more than once per day if seedlings are very fragile or the day is particularly hot. (Water any time the seedling appears to wilt or starts curling its leaves.)
Use mulches in beds and around plants to shade soil and retain moisture. Mulching or growing grass and other sun-loving ground covers on paths will also help to keep things cooler.
Sow shorter plants like lettuces, spinach or other shade tolerant species as edible mulch between larger plants like tomatoes and peppers. The tall plants will shade and protect the smaller plants, while short plants will return the favor by cooling the soil around taller plants' roots.