Don't worry too much about preserving balls - the scoring system in Toy Story: Smash It! isn't as tough as some of those in other physics-puzzlers.
Contact with anything collects boxes - balls, aliens, or blocks.
Press the left and right arrows to maneuver Buzz in those directions. This allows you to view puzzles from different perspectives. Doing this may reveal solutions you wouldn't have seen otherwise.
Don't aim directly for the aliens. They'll put up their shields each time.
Eliminating aliens is only half the fun. To receive three gold stars per level, you must also collect the floating blocks that spell out the word TOY.
Be on the lookout for exploding presents. You can solve many puzzles with one chain reaction.
Impact Balls can destroy just about anything. Throw the ball, then press the screen to make it travel in a straight line to the intended target.
Did you pull back on the screen to throw a ball and don't like the angle? Pull back even further (preferably towards the ceiling) to cancel the throw, or line up the targeting reticule with the white circle around Buzz.