Leave Puzzle Hints (in the settings) turned on. It doesn’t always point out the best move, but it will show you the best type of move available (four or more gems, skulls, etc.). It’s easy to overlook gem matches since you’re staring at a field of gems, so you may miss a match of four gems until the game suggests it.
Your normal priority (exceptions will happen!) for matching gems should be: any match that grants an extra turn, match three skulls, match three gems that grant mana to your troops, match three gems that deny opponents mana for their best troop.
Gain an understanding of how gems fall after being destroyed. You can really control the board (as much as the board can be controlled) by anticipating the fallout from matching different sets of gems. Is there a match near the top of the board? Check lower on the board in the same columns to see if there’s another match that, when completed, will cause the gems you’re eyeing to fall into place. Don’t match gems, no matter how tempting they are, that will give opponents an easy four-plus gem match. Unfortunately, there’s nothing you can do about the gems that fall in from the top to replace those destroyed by matches.