Dancer did this as a 4-H project in the area of indoor gardening. It is really simple to made a new plant from a one leaf of an African Violet although it takes lots of patience because the reward is weeks away from the initial planting.
To do this, cut the best looking leaf from the plant leaving some stem. Pick a leaf that isn't too old or too young. Cut the stem into a V on the bottom. Dip the end of the stem in water, rain water is best. Plant the leaf in a pot and put the pot on a saucer. Once a week, she chose Wednesdays, fill the saucer with water, don't water it from the top. Some things she saw about doing this said to put the pot in a plastic bag to make a little hot house for it. Fearing mold or fungal growth, she skipped this step. She only got one leaf so if that happened the whole project would have been for not.
In about two to four months the leaf will set up a good root system and should produce a baby plant next to the stem. We are excited now to see how long it is going to take to get a whole violet and the ultimate reward, flowers.