A korma is an Indian dish that originates in the northern area of the country and is said to be a legacy of the Mughal Empire. It is basically a spiced sauce in which meat or vegetables are braised, and relies more on sweet aromatics like cinnamon and cloves than on hot chilis for its characteristic flavour. Like much Northern Indian cooking, korma is popular with westerners because it tends not to be as spicy as other Indian cuisines. Korma's popularity is further heightened by the introduction of yogurt (or sometimes coconut milk), giving this dish a particularly creamy and cooling quality appreciated by wimpy white folks.
Like any food that is prepared in thousands of kitchens around the world, there are as many versions of korma as there are cooks who make it. I'm going to lay out the bare bones of ur-korma: korma at its most general. If you cook a lot, you can adapt this basic method freely; if you're a more timid cook, have a look at chicken korma to begin. But really I suggest that you be creative in your drive to make this, and every dish, your own.
As with most Indian curries, the preparation of korma begins by toasting spices; sometimes they are dry roasted, sometimes cooked in ghee (clarified butter). For true Indian korma, the use of ghee is more common. Begin by roasting aromatic spices in ghee (or oil). Try a piece of cinnamon, several whole cloves, and a few green cardamom pods which have been lightly broken open with the back of a knife. Once the spices begin to darken and release their fragrance, add some chopped onion and minced garlic and fresh ginger; the addition of one or two Indian bay leaves is traditional, but you may have a hard time finding them. (Variation: process the onion, garlic, and ginger with some almonds or cashews in a food processor to make a paste before you cook it; very yummy.)
Saute this delicious mess till the onions are softened and golden. Then a small amount of whole black cumin or regular cumin seeds, some fennel seeds, maybe some coriander seeds and saute for about a minute. (If you don't like whole spices in your korma, toast them separately first in a dry frying pan and then grind them up in a mortar and pestle.) Garam masala is another not-uncommon spice addition, and if you like spicy food, throw in some hot pepper flakes. You can also add ground almonds or cashews at this stage.
Now begin to add a cup or so of yogurt (or coconut milk), a little at a time, stirring all the while. And then the meat or vegetables make their entrance. Chicken is perhaps the best known protein addition in the west, but any kind of meat may be added, cut into bite-sized pieces. Vegetarian kormas with potatoes and peas are quite delicious as well, but I'd think any interesting-sounding veggie combination would be worth a try; just make sure that everything is cut into bite-sized pieces, and add harder veggies like potatoes and carrots first, reserving softer ones like beans or peas to add later on, when the hard veggies are softened. The whole thing should simmer for at least 20 minutes after the addition of meat or hard veggies.
Garnish the finished dish with chopped coriander and toasted slivered almonds, and serve with rice or Indian breads such as parathas.