Caliper

I find the dismount the least graceful (and I'm not coordinated enough to use Sheldon's method!). On freewheeling bikes, you are probably used to unclipping one foot and coasting as you stop then putting the unclipped foot down. With a fixed gear, I do find that I can't get the same "stop exactly where I want" sort of thing, but I do unclip one foot while slowing and then while the clipped-in foot is coming past the 6:00 position on the upstroke I will come off the saddle and use the clipped-in foot to backpedal and help with the final stop as I put my free foot down.

Starting is just like any other bike except that instead of using the freewheel to help position my pedals for starting, I will apply the front brake, push forward on the bars to lift the rear wheel off the ground and then use my clipped in foot to position the pedal. At that point, you are ready to start off. Getting the other foot clipped in may take a bit of practice if you are used to clipping in while coasting. Mentally getting over the habit of clipping in at a certain point in the pedal rotation may help. The pedals are rotating at a very consistent rate though, so with a quick glance down I find I can often catch the pedal wherever it is in its cycle.