To slide tiles, click and hold the left mouse button above one and move the mouse a bit. Arrows will appear in the direction(s) you can slide the tile, just move the cursor over and release. For tiles to disappear they must come to rest next to each other, meaning you can't send one flying past its match and expect it to disappear. And you can only slide tiles that aren't locked in by other pieces on the board.
The real fun begins when you factor in the delete option at the bottom of the screen. Each level lets you remove a limited number of tiles by simply pointing and clicking. You can only destroy tiles you can slide, so forget about digging to the bottom of the pile. It comes in handy in a pinch and adds a bit of unique strategy to the game.
A good puzzle game with an elegant presentation. There are only a handful of levels now, which is unfortunate, but it's a lot of fun while it lasts.