Line plate with paper towels; set aside. In 12-inch skillet, pour oil until 2 inches deep. Place deep-fry thermometer on side of skillet so bottom of thermometer reaches nearly to bottom of inside of skillet. Heat oil to 350°F.
Remove dough from can; shape into a ball. Divide ball into 4 equal pieces; roll each piece into a ball. With hands, flatten each ball into 4- to 5-inch-diameter disk. Poke about 1/4-inch hole in center of each disk (this keeps dough from puffing too much during frying).
Carefully drop disks of dough, 1 or 2 at a time, into hot oil. Fry about 2 minutes on each side, turning over carefully with slotted spoon, until outside is deep golden brown. Remove from oil with slotted spoon; place on lined plate so paper soaks up excess oil. Make sure oil has returned to 350°F before frying next batch.
For savory fry breads, immediately top breads with cheese and other favorite savory toppings. For sweet fry breads, top with honey or powdered sugar.