Choose one or more open-pollinated varieties of sweet corn to breed. You can either breed one variety with itself to keep it pure or combine two or more varieties, hoping to create corn with the best qualities of each. Avoid corn marked "F1 hybrid," since it may not breed true and will give unpredictable results.
Plant the corn, marking which row contains each variety if you're breeding several together. Plant longer-season varieties earlier than shorter-season ones, so they'll produce pollen and silk at the same time. You can also plant additional corn every two weeks to spread out the time that each variety will be at the right stage of maturity.
Cover the ear-shoots with clear plastic bags as soon as the green shoots become visible, before you can see the silk at the tip. Fasten the bags so they won't blow off, but allow room for the ear to grow inside the bag. Watch for the silk to emerge, since that's when the ears will be ready to breed.
When the silk is visible, collect pollen from the tassels of the cornstalks that you want to cross with those ears by placing a bag over each tassel. Tie or tape the bag shut, to capture the pollen that the tassels will release during the next day. Tassels produce pollen for many days, but one day's worth is enough to pollinate an ear.
Bend each tassel down on the following day, shake it to release the rest of its pollen into the bag, and remove the bag that should now contain a day's worth of pollen. Shake the pollen over the silks. You're done with the tassel bags now, but you must replace the bags over the silks to protect them from other stray pollen while the silk is still green. Once the silk has turned completely brown and dry, you can remove the bags.
Let the ears mature on the stalk until the husks are no longer green and the kernels are hard. Pick and label the ears and store them in a cool dry place until next spring, when you can plant the kernels to produce the first generation of your specially-bred sweet corn.