Always look ahead for your next move. Remember: if you run out of valid moves, the game is over. So check carefully to see whether your move will open additional linking options (good), reduce your available links (bad), or leave you without any further places to make links at all!
Also remember that matching a set of three links on the bottom of the screen will affect all the links above it, so if you can see two valid places to make a set of links, consider the top one first.
Cascades score extra points! The more cascade links you can make with a single move, the more the bonus points rack up. Look for moves which will cause the links above to fall down into more ready-made sets.
Connecting four or more links will give you more points than just three, but if you are playing in Puzzle mode, be careful. Sometimes you can more effectively clear a puzzle by clearing less than the maximum possible. If you have only 6 of a certain color in a puzzle, clearing four will leave you with an impossible-to-clear pair!