Focus on placing a high-value card in the corner and surround it by more high-value cards, limiting the number of directions you have to move everything.
Try keeping high cards together to make easy matches, rather than letting a bunch of low-value cards come between them.
Avoid letting the little guys hang around too long, so match them up to increase the value of your cards in play.
Make it a habit to slide a card in a given direction to get a better idea how things will go, then slide it back to its original position without removing your finger from the screen. This can occasionally make the best solution easier to see.
Unlock most puzzle games of a similar nature, you're not working against a timer so feel free to take your time.