I have a cooler that holds 7 gallons and happens to be the *PERFECT* size for brining 1-2 14-pound turkeys...which was totally a happy accident since I bought it because it's also the perfect size to hold 2 gallons of milk and one bag of ice for road trips (it's a Coleman model 6277 if anyone cares). You could easily do this in a 5 gallon bucket or a massive stock pot, or, well, really anything that the turkey will fit inside completely.
My brine is super simple, and you can omit the beer and just add extra water if you'd like and it'll be just as good.
In a large pot, combine:
6 12-oz beers
1 cup of brown sugar
2 cups of salt (whatever salt you have....I use kosher in my cooking, but I always just buy a 50 cent thing of cheap table salt for this....that is almost exactly 2 cups)
2-3 quarts of water (enough to top off the pot)
Heat over medium high heat until all of the sugar and salt dissolve, then remove from the heat and allow to cool completely. If you are as impatient as I am, you can pour this over a bag of ice right into the bucket/cooler/pot you're going to use.
Pull the pop up thermometer out of the turkey if there is one, rinse well under cold water, and then put your turkey into the cooler breast side down. Add a bag of ice, and then top off with water and stir to distribute the brine. Let the turkey sit in this at LEAST 8-12 hours. Usually, I buy a frozen bird and I let it thaw in the brine. This saves me room in my refrigerator, and it gives the bird extra time in the brine solution. :) Win-win! Just make sure you check at least once a day and add ice as needed, to keep everything cold. Luke warm water + poultry is not a good idea. ;)
When you're ready to cook your bird, preheat your oven to 500 degrees. Pull it out of the brine and rinse it off, inside and out. Pat it dry and put it on a rack inside a roasting pan. Smear the outside with real butter (you could certainly whip your butter up with some fresh garlic paste and use that for extra flavor) and put stuff loosely inside as desired (note: NOT STUFFING. STUFF. Onions, garlic, carrots, celery, apples, orange peel, whatever...but under no circumstances dressing...It will not cook evenly and will just make a huge yucky mess). Put extra 'stuff' in the bottom of the roasting pan and add about a quart of chicken stock (or turkey, if you happen to have it in your freezer...I never do). Just make sure the bottom of the turkey is not touching the liquid--you can add more stock as necessary throughout the cooking process if you find all of the liquid has evaporated. You can just as easily use Better Than Bouillon and hot water, too. ;)
Throw the bird into the 500 degree oven, close the door and walk away for 30-45 minutes. Do not look at it. Do not, under any circumstances, open the door. After 30-45 minutes, turn the heat down to 350, pull it out, baste it really good with the liquid in the bottom of the pan, and then tent the breast only with foil. Put the bird back in. Every 30ish minutes, go back and baste it again.
Using a probe thermometer (available at Walmart for like $3....don't skimp), take the bird's temperature in the thickest part of the thigh, between the thigh and the body of the bird. When it reads between 155 and 160 (should take roughly 2-3 hrs for a 13-15 lb bird), pull it out and cover the entire turkey tightly in foil. Its temperature will continue to raise and the juices will distribute it will be perfect and ready to eat after about 20-30 minutes.