Nothing beats the smell or taste of that perfectly smoked brisket. It's a most satisfying and memorable experience to see the happy smiles on the faces of satisfied guests at a backyard grill fest.

[edit] Steps

Choose your meat. Look for a brisket with a substantial fat layer and good marbling of fat in the meat. Point cut will likely be better, but flat cut will suffice if well marbled.
Rub your favorite seasonings such as garlic powder, onion powder, paprika, etc. deeply into the meat. Often brown sugar is added to the rub, for that bbq sweetness.
Use "indirect heat" method of cooking on a grill by either pushing all the coals to one side and cooking on the other, or only lighting one side of a gas grill.
Remember to place soaked hardwood chips over fire before placing the meat on the grill rack.
Add a drip pan below where the meat will sit, as a fair amount of fat will cook off of it.
Place brisket on grill, fat side up, not directly over heat.
Maintain a grill temperature between 200 and 250 degrees, the closer to 200 the better.
Let the meat smoke for several hours (at least 4, preferably 6 to 8), rotating it 180 degrees in the middle of the cooking cycle.
Remove to cutting board and slice across the grain.

[edit] Tips

Of course, the wood chips should be soaked in water for about an hour before placing them on the grill fire.
Replace wood chips as needed. The smoke gives the meat flavor and the moisture helps in cooking, so don't let them run out.
If you have a small grill (or an exceptionally large slab of meat, or multiple briskets) create a heat shield between the fire and the meat with heavy duty aluminum foil. Do it in a way that keeps the direct heat off of the goods, but doesn't impede air flow (we are trying to immerse the meat with smoke, of course). Rotating the meat occasionally will also prevent one side (or piece) from cooking more than the others.
If you are using a gas grill, purchase a smoker box to hold your wood chips, or nest them in two layers of heavy duty aluminum foil, with an open top, so that the smoke can get out.