I can't emphasis this point too much. I've read a lot of stories about people brining a turkey only to end up with something that was too salty to eat. I rinse the turkey thoroughly, then I submerge it in cold water. And make sure that you rinse out the inside as well. Every surface needs to be rinsed.
Once you turkey is rinsed (did I say that already?) you can prepare it as normal. One word of caution. While the turkey will not taste salty if your rinsed it properly you do not need to add salt to this turkey. If you are using a spice rub or seasoning on the turkey, do not add salt. If you are going to be stuffing the bird, use a stuffing that doesn't have any salt.
Otherwise you can now enjoy a great turkey no matter if you smoke, grill, fry, or even roast (if you must) it.

