Contrary to the implication of the name, Boston butt isn't actually a rump roast; this low-cost, fatty cut comes from a hog's shoulder. In Revolutionary War times, cheap pork cuts were kept in barrels called butts, probably accounting for the name. Although brining offers the most benefit to lean cuts, it enhances the finished product when preparing a Boston butt, too. Soaking the meat in a saltwater solution adds moisture to it, so it experiences less drying out and shrinkage due to water loss during cooking. Brining also offers an opportunity to impart more flavor into the pork.
Select a nonreactive food-safe container that's big enough to soak the Boston butt in, with the meat completely submerged. With the notable exception of stainless steel, most pots and pans are reactive, so they aren't suitable; glass, ceramic, plastic and stainless steel are appropriate choices for brining.
Fill the container with enough liquid to immerse the Boston butt. This can be all water, water mixed with another liquid, or another liquid altogether. If choosing something to use with or instead of water, pick something with a flavor you want to impart into the pork. Wines, beers, teas, vinegars, fruit juices, stocks and soy sauce are all possibilities. The more you use, the stronger the flavor imparted.
Stir in about 1 1/2 cups of kosher salt or 2 cups of crystal kosher salt per gallon of liquid, with a spoon until it is fully dissolved. Table salt works, too -- but you must use non-iodized salt, which isn't usually what people have at home. If you do use non-iodized table salt, use only about 1 cup per gallon of liquid.
Season the brine with other ingredients, if you wish. Only water and salt are necessary, chemically speaking, for the brine to work, so other liquids and additional ingredients are optional, used purely to enhance the Boston butt's flavor. Consider a sweetener; use about 1/2 cup of sugar, brown sugar, syrup, honey or molasses per gallon of liquid. You can include complementary fresh or dried herbs and spices to taste, as well.
Immerse the Boston butt in the brine. Top it off with a little water or other liquid, as needed, if the meat isn't covered completely. Put it in the refrigerator for six to 12 hours. Discard the brine after use, as its high salt content precludes it from you using it as a sauce. Additionally, the brine has been contaminated by raw pork, so it is not safe for you to use the brine, and you must discard it.