These are my favorite- Raised Donuts.

Mix together
1 cup lukewarm milk
1/4 cup sugar
1 teaspoon salt
Add:
1 package yeast
Stir in:
1 egg slightly beaten
1/4 cup shortening
Add:
3 1/2 to 4 cups flour

Knead dough until smooth and elastic, 5 to 10 minutes. Put in greased bowl, cover with a damp towel and let rise until double in size.

Punch dough down and roll to a thickness of about 1/3 inch. Cut with a 3 inch doughnut cutter or a round circle, punch out the center, (about a 1 inch circle). Let rise until light, about 30 minutes. Drop in hot deep fat (375 degrees). Cut until golden brown on both sides. Drain on absorbent paper.

At this point, they can be rolled in confectioners sugar, plain sugar, cinnamon sugar or glazed.

To Glaze:

Add 1/3 cup boiling water to 1 cup confectioners sugar. Mix well and dip hot donuts in.

I have some other recipes for donuts, but a quick one is to use canned biscuits, tear a hole in the center and fry.