Key lime trees are best grown in semitropical to tropical climates, but they can be grown in climates with cold winters as long as they are brought inside during the cold season. You can choose to either grow the lime from seed or as a sapling, but growing from seeds takes longer to produce fruit. It is this reason why many gardeners choose to plant a sapling.
Plant a key lime tree sapling in a large planter (at least 5 gallons), and fill in around the roots with light potting soil such as perlite.
Place the planter in a full sun area where the soil will stay warm and moist. It is ideal to keep the key lime tree in a planter so you can bring it inside for colder seasons.
Remove any small branches that grow within 8 inches of the soil with pruning shears as you monitor your key lime tree. This is to help "train" the tree so it will create a thick main trunk.
Fertilize the tree each month with a fertilizer high in nitrogen content. Water the key lime tree regularly so the soil is kept moist, but you never want it to be soggy as overwatering will kill the key lime tree. Also, make sure the tree is well-drained.
Bring the key lime tree inside when the temperature drops below 50 degrees F in order to protect it. Place it in a sunny window, and decrease the amount of watering accordingly.
Keep an eye out for blooms and fruit on the key lime tree. This can take anywhere from a couple years of to almost seven. Make sure your tree is outside in warm seasons in order to be pollinated (as long as you want it to produce fruit) and keep the branches pruned properly.