You can use a 5 gallon bucket, a large cooler, the super large plastic bags, etc. for brining. I don't have room in my refrigerator to hold that large of a container so I keep ice (in plastic bags) or frozen cold packs in the container. Check your ice regularly to make sure you are keeping the turkey cold enough.
Do a Google search for brining solutions. You can add all kinds of things to give you the taste you want such as citrus, spices, onions, garlic, etc. I used Martha Stewart's recipe last year.