The way to play is by swiping across two tiles to make them exchange places. This is only possible if doing so will create a line of at least three tiles. That limitations ensures that you can't just shunt a specific tile across several rows or columns to make a line.
As with similar games, you can create chain reactions and clear a clear huge amount of tiles, doing this will earn combination bonuses. However, setting up combinations can be a distraction from clearing the jewelled tiles. The faster they are cleared, the greater the amount of gold you awarded at the end of the level.
Gold ties into the meta game surrounding Treasures of Montezuma 2. There is a 'world map' where you have to build specific types of buildings, purchased with gold, before you can proceed into higher puzzle levels, and this is how the developers, HeroCraft, make some money from the game. For the impatient player, it is possible to purchase gold, via premium SMS, allowing you to rush through to higher levels.