Once the dough has risen, punch it down and roll it out on a floured surface to about 1/2 inch thickness.
Use a doughnut cutter or two round cutters (one larger and one smaller for the hole) to cut out the doughnuts.
Re-roll the dough scraps to make more doughnuts.
Fry the Doughnuts:

Heat vegetable oil in a deep fryer or large pot to 350°F (175°C). Make sure the oil is deep enough to submerge the doughnuts.
Carefully fry the doughnuts in batches, making sure not to overcrowd the pot. Fry them for 1-2 minutes per side, or until golden brown.
Use a slotted spoon to remove the doughnuts from the oil and place them on a paper towel-lined plate to drain excess oil.
Cinnamon Sugar Coating:

In a shallow bowl, mix together the sugar and cinnamon.
While the doughnuts are still warm, toss them in the cinnamon sugar mixture until fully coated.