Kaffir lime leaf is a key ingredient in Thai cooking as well as other Southeast-Asian cuisines. It is probably one of the most aromatic of all herbs and a wonderful addition to many Thai and Southeast-Asian soups, curries, and stir-fries. The thick leaves are dark green and shiny on one side, and pale colored and porous on the other.
Kaffir lime leaves are not the same as leaves from a regular lime tree. Kaffir limes (Citrus hystrix) are different from regular limes in that they are very bitter with bumpy skin. In Thailand, the kaffir limes are not consumed but are used mainly in producing household cleaning products. The leaves are very aromatic and can be consumed if cooked or very thinly sliced. They are hourglass-shaped "double" leaves, meaning there are two leaves at the end of the stem.
Kaffir lime leaves can be purchased fresh, frozen or dried from Thai or Vietnamese food stores (some Chinese food stores carry them while others do not). In Asian food stores, you'll find them either in the fresh produce section alongside the other herbs, or in the freezer section. A few of the larger regular supermarket chains in the US and Canada are also starting to sell lime leaves—look for them in the fresh herbs section.
Note that dried lime leaves are not as aromatic or flavorful as fresh or frozen. One package of fresh lime leaves will last you a year or longer, and they freeze well. Take one or two leaves out as you need them, then wrap up the package and return it to the freezer until next time.
Think of kaffir lime leaves as the Asian equivalent to bay leaves. They can be added whole to Thai curries, soups, and stir-fries (and removed before eating the dish), and can also be cut up into very thin slivers and added to spice pastes, or used as a topping for many recipes.
If still attached to the stem, remove the leaf by holding onto the joint between the two leaves and tear away the leaf. The best way to prepare lime leaves is to cut them very thinly (into sliver-like pieces) with a pair of clean scissors, discarding the central stem/vein. Frozen lime leaves can be used right away, or briefly rinsed under hot water to thaw and bring out the fragrance.
Many Thai recipes feature lime leaf as a key ingredient, such as chicken stir-fry, green curry, chicken fried rice, and Thai steamed mussels. If a recipe calls for kaffir lime leaves and you cannot find them, or choose not to use them, do not substitute with another ingredient—skip it. There is no replacement for the unique flavor the kaffir lime leaf imparts to a dish.