Unlike most citrus, the rind is consumed, and it's actually the sweet part of the fruit. Kumquats make great candied fruit, but you have to cut them in half first, horizontally, and remove the one or two gigantic (in comparison to the size of the fruit) seeds.
But to use them raw in salads, or on top of chicken, fish or short ribs, they need to be thinly sliced. My favorite method for doing this is to slice off just enough of the stem end to get rid of the stem, slice thinly until you come to the seed(s), remove the seeds, cut another slice or two, turn and slice the other end until you can no longer slice the fruit thinly. Pop the remainder in your mouth and start on the next one.