My family won't let me smoke a turkey without it. You can put a dark brown on the skin, cook the bird thoroughly and the meat will still gush juice when you slice it. No comparison to dry smoking. Best ever.
Being able to submerge the bird in a 3- to 5-gallon bucket in a refrigerator is easiest, but if you're short on space, use a 2-1/2 gallon ziplock bag.
Put the turkey in the bag and place upright in an ice chest. Fill bag with brine to cover bird and zip bag. Keep chest iced overnight and smoke bird tomorrow.
Caution: no matter the brand, the ziplock zipper will not withstand the weight of a turkey and 2-3 gallons of brine. Just sayin'.
If your chest is big enough, you could use a food grade plastic bucket and put your ice outside the bucket. Don't dilute the brine.
Two notes: Don't use a trash bag for the brine and anyone who is on a reduced salt diet may find the smoked bird too salty. People who consume the normal American diet say it does not taste salty at all.