To move the tiles, swipe up, down, left, or right.  A swipe with three similar tiles in a row or column will score and merge the three tiles into a single tile with three times the value.  On a scoring move, the two tiles that are eliminated are replaced with randomly placed "5 tiles."  A non-scoring swipe will add a new "5 tile" at a random location.
A swipe with two or more scoring rows or columns will populate fewer "5 tiles" as a bonus.  Also, a swipe with a full row or column of identical tiles will populate even fewer "5 tiles" as an extra bonus.
The game ends when there are no more scoring or non-scoring swipes on the board.  A good game will last about 10 minutes and can achieve upward of 20,000 points.
Tiles that can be achieved:
5
15
45
135
405
1215
3645
10935
32805
98415
295245
885735
2657205
...
...
Enjoy!