It depends on who won the previous end. Winner leads off, therefore loser gets last stone. A blank end means the status quo continues. Getting the last stone is called having the hammer. There is a lot of tactics in curling.
Thanks. The subtleties of it are a bit beyond me. However I have been watching it. I am inclined to agree with Aileen that a lot of the events in the Winter Olympics are bordering on the suicidal.