To get rid of moles, first find the tunnels the moles currently use. To do this, place an object that is not too heavy onto the nearest molehill, and check it in several days. If moles use the tunnel, the object is going to be removed from the hole. Mole traps are one of the most effective ways of controlling moles, so buy several traps, set them up in a tunnel, and wait for moles to get caught.
There are several types of mole traps available at hardware stores and online. Lure traps prove very easy to set up, as they only require placement in the tunnel. Circular rodent traps are suitable for other rodents as well as moles, but they require some digging. Loop choking style traps are the most effective ones, but their installation process is the most difficult. You can improve the effectiveness of traps by using baits with them. If you don't want to buy traps specifically for moles, try using mouse traps.
Another way to get rid of moles is to gas the tunnels. Be extremely careful when using poisonous gases, and make sure that your children and animals don't accidentally get poisoned. If you are lucky to gas a large mole nest, and if you repeat the process frequently, there is a good chance that you can get rid of moles completely.