How to Play Shortstop in Baseball

Position yourself correctly. The most common position is halfway between second base and the person that's playing third base.
Work on your range. A shortstop has to be able to get to many ground balls very quickly.
Build arm strength. A shortstop also has to have a strong arm to get the ball across the diamond to the first baseman. To do this, play "long toss" (throwing over 100-150 feet) for at least five minutes each time you warm up. Start slow and don't hurt your arm by trying to throw that far on a line. A nice arch is fine until you build strength.
Know your roles. If a ball is hit to left field the shortstop has to be the cut-off man on the play.

Tips:

Shortstops have to work hard on ground balls and throwing. They also have to take a lot of cuts in the batting cage. A good hitting and fielding shortstop can get you far. Also working out in a weight room (not for young kids under 13 or 14) and running a lot will build your body for baseball.
Remember, you can be the best shortstop in the world, but if you can't hit, you won't play. Become a well-rounded player.
In a lot of youth baseball many of the players wonder why the infielders cannot turn double plays every time like the majors. They only get the lead runner and the throw to 1st is late. This is all because your middle infielders are not positioned to turn a double play. The second base men should be 4 steps back and 4 steps over from second base, and the shortstop should be about 5 steps back and 7 over on a right handed batter. (These are you normal steps not long strides and yes, it looks really close but that's where you should play to turn two). With decent transitions you'll find that you will be turning a double play A LOT more often.