Smoke it the same as a turkey just watch the finished temperature....
Brining is best unless you purchase an enhanced breast, then do not brine.
Rub the turkey with olive oil or butter and apply your rub.
If you want a nice looking turkey breast, place the dry breast into a stockinette bag and hang, this allows even smoking. The can be purchased cheaply from the Sausage Maker in Buffalo, NY by mail order but they are not required.
I prefer to use Apple chips when smoking turkeys, hickory seems to gives the bird a strong smoke flavor and over-powers the flavor of the meat it self. Try and avoid any strong smelling woods to keep the turkey with a clean smoky flavor.
Set your smoker temperature to 300-325 degrees Until you reach 160 degrees internally in the breast. Test in at least two places (or more) and remember that turkey bones heat faster so keep the thermometer away from the breast bone. The length of this time all depends on the size of your breast. Once done, remove your turkey and rest for 30 minutes before eating. Once rested put the breast on the slicer and slice.
.