Here is how I brine a turkey. It is heavily based on Alton Brown's recipe, but tweaked to my taste. I like a moist turkey, but not too fruity or sweet. One year I tried a recipe that called for mostly apple cider as the liquid, but that was too overwhelmingly sweet for me.
Also, I use a oven roaster bag as a liner in a 5 gallon bucket. If you can't make the room in your fridge for the bucket, put the bucket in your unheated garage or back porch and keep an eye on it to make sure there is enough ice for the entire brine operation.
UPDATE: Since I am the only one in our home that eats turkey, I have downsized the bird to a 4.5-5lb. boneless turkey breast. This means I only need about half of the brine and it fits in a large stockpot in the fridge.
Turkey Brine(per gallon of water):
1 cup Kosher Salt
1/2 cup brown sugar
1 orange quartered
1 lemon quartered
1 gallon vegetable or chicken broth
3 sprigs of thyme
2 sprigs of rosemary
1 tablespoon black peppercorns
1/2 tablespoon all spice berries
Once you have determined how many gallons of water you need to immerse the turkey fully, add appropriate amounts of above ingredients in stock pot and slowly bring to a boil. Remove from heat and let cool to room temperature and refrigerate if not using immediately.
Combine brine and ice water in appropriate sized container. Place thawed turkey (breast side down, innards removed) in container ensuring bird is fully immersed. Refrigerate for 8 to 24 hours.
Remove turkey from brine and rinse thoroughly with cold water. Pat dry and apply canola oil to skin. Roast at 500F on lowest rack for 30 minutes to brown skin, then reduce heat to 350F and cook until internal temp reaches 161F (internal probe inserted into breast.) Remove from oven and cover for 15 minutes before carving.
Original "Good Eats" recipe by Alton Brown: