Because I avoid all chemicals and toxins in the garden, I'm not left with a whole lot of alternatives to eradicate these evil insects. The most powerful thing I use is Safer Insecticidal Soap and frankly, I've found it does nothing to deter them. I'm sure there's stronger stuff out there that will do the trick, I'm just not willing to use it. It's also been suggested to me that I use beetle traps but that is an idea that just grosses me out beyond words. Plus, it's my understanding that they attract more beetles than they actually trap which would seem to only exacerbate my problem rather than mitigate it.
Usually I see evidence of the beetle before I see the insect itself. You'll know if your leaves look like the ones below. They eat away at the foliage between the leaf veins. Ultimately you are left with a leaf that looks like very delicate lace. Apparently, the folks in Kentucky have a wicked problem with Japanese Beetles because the University of Kentucky's College of Agriculture has done extensive research on them. I also found a good site at Ohio State University. Both say that the beetles are attracted to particular odors and get really active in direct sun. And they list plants and trees that are susceptible to damage by them.
In the end, I just let them be and live with the damage--it's not like they are munching on every single thing in my garden. The life cycle is 30-45 days and every year I expect them to show up in mid-June and disappear at the end of July. That's not to say that they don't leave a whole lot of destruction in their wake. But I cut off the damaged foliage (in the case of my sweet potato vines, I cut off a lot) and new, healthy growth reappears in short order.
Bookshelf: Container Gardening Books