While fried dough not a new innovation (fried breads have probably been around as long as humans have had flour and some sort of oil), the American fry bread tradition dates back to the atrocities inflicted on Native American Indians in the late 1800's. The rations they were given when they were forced into camps were very non-traditional to them and not the best quality, but they made do. The delicious fry bread we enjoy at Fairs and in Indian Tacos is a quiet legacy of the tenacity and endurance of those Peoples.
There are lots of traditional Indian fry bread recipes; I'll link some below if you'd like to try them out. I looked at the basic needs and techniques and faked some lovely fry bread. The fry bread at the Navajo Hut at the Fair is better, but my kids liked this just fine.
Fill a heavy pan with enough oil for frying. The oil should be deeper than your dough is thick; you could also deep fry. Cast iron is recommended in a lot of recipes. Get the oil hot enough to fry - test the oil by dropping a pinch of dough in it, the dough should bubble immediately.
While the oil is heating cut the dough as big as you want the fry bread, but no bigger than what you're frying it in.
Place the dough in the hot oil and fry until it floats up; turn it and fry a couple more minutes until it's brown on the bottom. About 3 minutes a side worked for me.
Put the hot dough on paper towels to drain and sprinkle with powdered or granulated sugar if desired. Best eaten warm. It makes a good bread for scooping or dipping and an excellent dinner side dish.
You could use any bread dough you have handy if it's ready to bake. I completely cheated and bought a tube of Pilsbury Thin Crust Pizza Dough. My tendinitis just won't let me knead dough any more. I chose pizza dough because it was conveniently already rolled out thin. I unrolled the pizza dough on my big cutting board and made 4" squares (more or less).
Other bits I learned during my research:
"Bannock" is fry bread. I'd read the word but never looked it up.
Eskimos have fry bread! Bad Alaskan me, I feel like I should have known that.