Sprinkle yeast over warm water (110 degrees, about 50 sec in the microwave) and let the yeast activate for 5 minutes.
Cream butter and sugar. Then add the eggs and salt.
Add the activated yeast and flour into the creamed butter mixture. Knead with dough attachment in a stand mixer, or on the counter until the dough is smooth
Place the dough in a greased bowl, and let it rise until it has doubled, about an hour.
Once the dough has risen, roll out into a ½ inch thick sheet. Cut into rectangle shapes or use a cookie cutter to make traditional donut shapes.
Let the cut dough rise for another hour.
After the dough has risen for a second time, fry in oil. Use a candy theremometer to make sure the oil stays at or around 375 degrees. Fry for 1 minute, then flip over the donut and fry for 1 more minute.
Remove the doughnut from the oil, onto a cooling rack and paper towel to remove excess grease.
Allow the donuts to cool before frosting.