When I'm in Louisiana visiting family, I eat them... straight off of the tree. The pulp center is tart, but the sweetness is in the skin, and the longer you chew, the sweeter it gets.
The round variety is primarily used to make marmalade or jelly. The oval kumquats can also be made into marmalade, etc. but is also the variety that most people eat like any other fruit.
"Food is our common ground, a universal experience." - James Beard