Lime is native to Asia but is grown throughout the world where the climate allows. Limes like lemons like warm sunny spots (at least 6 hours of full sun per day). Some can tolerate colder climates like UK etc. In colder climates, it is better to grow limes in large pots that can be brought indoors or under glass over the winter to prevent the cold from damaging the plants. Limes are grown mainly for their citrus fruits, but the leaves can you used to make tea.
Most people start by buying a small established lime tree. This can be planted in the ground or large pot with good quality compost. Lime trees can also be grown from seed but it will be about 5 years before you will receive limes this way. It is worth removing fruit from young trees to allow the tree to focus on developing a strong root system. Lime trees often get affected by iron deficiency (yellowing of the leaves). To prevent this it can help to water them twice a year with iron chelates. For a good harvest, it is important to regularly feed your lime tree with a flower or fruit fertiliser.
Once the lime bugs have appeared it can take between 6 and 9 months for the fruit to grow and ripen. Limes can be tricky to tell when they are ripe. But they do tend to go a lighter green when they are so watch for this change. Also if you lightly scratch the skin of the lime you will smell the limey citrus smell when ripe.