What is the most effective way to rid your lawn of moles?
There is no effective way. They are living below ground and we are above it.
You can try:
Products that are repellants like Mole Med and Scoot Mole that are castor oil based that are sprayed on and watered into the lawn.
Products that are poison baits like Mole Patrol and the gummy-worm poison bait. There is always a danger of dopey dogs digging them up and eating them with bad results. There are also poison peanuts that do not work... except on a dog.
There are traps like a spring-platform, scissors or choker loop traps. You have to set these on active runs. The second and third listed traps work the best.
Or buy a lawn roller that is weighed down with water inside. Add enough water to cause the trails to be flattened but not leave a ditch in the yard. Most mole tunnels are used once and never again. The grass dies because the roots are hanging into an air space below ground.
A mole's diet is 80% earthworms and 20% soil insects and grubs. Grub treatments do not get rid of moles.