Shaking Relics
Getting good at "Jewel Quest 2" means concentrating enough to find the next move before time runs out. However, if you're having trouble finding moves, you can always wait a moment and look for any shaking relics or jewels. These will show you where there are possible moves.
Two Buried Jewels
Look for two jewels of the same color buried along the grid. Even if buried, these jewels can form part of a match, and thus increase your point value when looking for potential moves.
Coins
Matching three coins with each other will not only clear that part of the board, but also give you what's called a "special move." You can use this special move to break buried pieces out from their hiding places, making it much easier to match them up with similar pieces on the grid.
Save Special Moves
If you're just getting used to the game, it's okay to use your special moves as soon as you attain them. However, if you are getting more experienced, it's often a good idea to save these special moves for later levels when there are more buried jewels and more difficult board layouts.