When covering second on a double play, the most natural way to make the out and positon yourself to throw to first, is to approach the bag and straddle it. As the ball is being thrown, catch and drag your right foot across the bag to make the out. The motion is kind of a hop where you will drag your foot then perform a hop to position yourself out of the path of the runner and squared up to throw.
Time your approach to second so you can go any direction to catch the ball. The best way to do this is to hustle toward the bag and then as you get closer take smaller steps to help you get to the bag as the ball is being delivered. If the ball is on target you can continue across the bag and make the throw. If the ball isn't on target you still have some room to make an adjustment.
If the ball is thrown on the inside of the bag, you can use your left foot to make the out and then push off toward the inside of the bag to clear the baserunner and make the throw. This play is much more difficult for a shortstop to master because it's hard to get your body lined up to make a throw. Younger players will need to push off and then take a step or two to get lined up and throw. Older players with stronger arms should be able to push off and rotate on their right foot to make the quick and accurate throw.
Sometime the ball will be delivered before you can get close to the bag. In this case you can catch the ball and then use your lead throwing foot to make the out. Simply step on the bag as part of your normal throwing motion. You will make the out at second and the bag will provide you protection from the baserunner.