No no no no. You cook it until medium rare or medium.
Score the fat and place it fat side down in a cold pan. Put it on low-med heat and render the fat, removing it little by little before it pools and burns. Let the fat cool and put it in the freezer. Duck fat is gold! Pull it out on special occasions and pan roast some potatoes in it, your guests will thank you by drooling all over your dish.
After removing most of the fat then you can start to season and layer flavors on your duck breast. I personally like seasoning it with salt, pepper, and allspice and then drizzling it with a little bit of honey near the end of cooking. Also instead of honey you can deglaze the pan with vermouth and then add fresh blackberries and reduce for a minute or two. Let it rest before slicing
The basic approach to duck breasts is as Koukouvagia says; that is, score the skin and fat (without cutting into the flesh) and sear out the fat. Flip the breast over, and finish in the oven, with whatever other ingredients and flavorings you might care for.
One of my faves is Anne Burrel's Duck Brasts with Clementine Sauce and Kale. You can find the recipe over at the Food Network site.
My approach, which I got from Alfred Portale, is similar but, in my opinion, easier. Pat the breasts very dry with paper towels. Season both sides as appropriate -- anything from just salt and pepper to a complex Cajun mixture, whatever you like. Score the skin in a diamond pattern with a very sharp knife, trying not to quite hit the flesh but certainly not scoring the flesh. Lay breast(s) skin-side down in a cold, heavy pan, and turn the heat to medium. Wait 10 minutes, at which point the skin will be golden-brown and crisp, and they will have released from the pan. Flip the over and continue to cook 3 minutes. Shut off the flame, remove the breasts to a warm dish, cover and let rest 5 minutes. Wait about 30 seconds, then pour the clear fat through a fine strainer into a heatproof bowl. [Incidentally, if there is any golden-brown crusty stuff on the bottom of the pan, you're in luck: put the pan over medium-high heat, wait until it stops spitting, deglaze with a little brandy or white wine, and you've got a perfectly respectable sauce base to add to whatever you're making.] When the breasts have finished resting, slice on a bias and they will be beautifully rosy-pink in the center.
I have no idea why it is, but I have done exactly this with breasts from quite different sorts of domesticated ducks, of very different weight and fatness, and it always works. The only things to watch out for are:
1. The skin must be quite dry or it may stick.
2. The pan needs to be pretty heavy and even-heating.
3. Flip the breasts when the skin is done perfectly, not before or after. Ignore the clock. Once they're flipped, the timing --- 3 minutes cooking, 5 minutes resting --- seems to work perfectly. But usually it's going to take just about precisely 10 minutes on the skin side.