If you are stuck, use the hammer to strike a stone. However, use this powerup sparingly as it is quite scarce. You only want to use it when you really can't go any further. You can also click on the shuffle icon, this shuffles the playing field so that all stones are random again. This is also very useful if you cannot go any further and is cheaper than the hammer. With the brush power up you can make stones a different color. You understand that this power up is quite powerful. It is therefore the most expensive of all.
Each level has a goal, so the first level has the goal to get 1200 points. Achieve these goals to advance to the next levels. The level stops when no more combinations are possible, even if you have already reached the goal. So keep playing until nothing is possible anymore, this just gives you more points.
Are you getting a bit further in the game? Then there are diamonds, these turn a different color each turn. So strategically wait until it turns a color of the surrounding stones and play away as much as possible.