Whether you've brined it yourself or you've purchased a piece of cured but still raw corned beef, cooking it slowly is the key to ending up with a tender, flavorful meal. There are a few ways to cook corned beef. Note that corned beef is often sold already cooked. If that's the case, you'll just need to heat it up, not fully cook it as described below.)
Boiling is the traditional way of preparing corned beef for a reason: It cooks the meat, tenderizes the tough cut of brisket usually used to make corned beef along the way, and it draws out the excess salt (used in brining) that gives corned beef its flavor and texture—and it does all three of these things at once.
Put the corned beef in a large pot and cover with plenty of water. You can add a tablespoon or two of pickling spice as well as a few garlic cloves, a quartered onion, a carrot, and a few stalks of celery to the mix if you like, but they're not required. Bring everything to a boil, cover, and reduce the heat to maintain a steady simmer and cook, more or less undisturbed, until the corned beef is completely tender when pierced with a fork, 3 to 4 hours. Remove the corned beef from the pot and slice across the grain to serve.
Note: You can add potatoes and/or cabbage about 30 minutes before the end of the cooking time, if you like, but you can also wait until the corned beef is definitely done, pull it out of the pot and cover it to keep it warm or even set it in a 200 F oven, cook whole small red potatoes and cabbage cut in wedges in the liquid until they are done, and serve everything cooked to its ideal done-ness.
Cooking corned beef in a slow cooker has all the benefits of boiling corned beef, with the benefit of not having to stay home while it cooks. Place a quartered onion, a carrot, a couple of garlic cloves (if you like), and a few stalks of celery in the slow cooker. You can add potatoes, too, if you'd like to serve them with the corned beef. Set the corned beef on top of the vegetables, sprinkle it with a tablespoon of pickling spice, and add enough water to just submerge the beef. Cover and cook on high for about 4 1/2 hours or on low for 8 to 9 hours.
Baked corned beef develops a fabulous crispy crust. Before you bake it, however, you really must boil it to remove some of the curing salt. So, even though you'll be baking it, put the corned beef in a large pot and cover with water. Bring to a boil while you also preheat an oven to 350 F. Discard the water and repeat. Seriously. You want to draw out more of the salt before you bake it. Set the corned beef fat-side-up in a baking pan and cover with foil. Bake for 2 hours. Unwrap, position an oven rack in the top third of the oven, and bake until the top is browned and crispy, about 30 minutes. Some people like to spread the meat with mustard and/or sprinkle it with brown sugar to add flavor and help the brown crust develop.