Easy. Remove their food source. Use a good grub and insect killer on your yard NOW. This is the right time of year. The moles eat grubs & worms. Removing the grubs will do a lot. The windmill thing is supposed to work. A cat is a great idea. Not only does it hunt them, if the cat pees in the yard that scent is a real warning to the moles and they tend to leave rather than get eaten.
VOLES are a different problem. They are vegetarians, and the grub killer doesn’t work. They are short tailed mice that burrow just a little under the ground and leave visible trails. Find out which you have. You might have both! Put a mouse trap with peanut butter bait by a hole or a trail. If you catch a short tailed mouse, you’ve got voles.
This works exceptionally well here in the northeast. I have a horrible mole problem when I don't do this and have NO mole problem when I do do this. I would add that you should reapply around July 1.
As a side note, we have a springer and a boxer/hound mix and both of them are great mole hunters. Of course, our lawn looks like a scale model of down-range artillery practice....