We also have a mole problem. The only thing that works for us it to use mole traps, purchase at a garden or hardware store. They are not unlike a large mouse trap. They are inserted down into the top of the mole hole. I hate doing this but death is instant. Otherwise a good hound dog works too. Please don't use poison, it is not only dangerous for other things but is an unpleasant death for the moles.
They are really tough to get rid of. As others said, installing traps is the tried and true solution. You have to monitor them and move them as needed based on where the moles are moving.