Kill by squishing them or dropping the caterpillars into a bucket of soap water. Power spray them out of the trees - even the big caterpillars seem pretty fragile. Wrap your trees with fabric (something inexpensive like burlap works just fine).
The fabric works like this: the caterpillars feed at night, and then climb down the tree during the day to get out of the sun - and presumably hide from predators like birds. At night, when they climb back up the tree to feed, some will get caught in the fabric. Others will use the fabric as a resting place where they are hidden from predators. When checking the fabric in the morning, it will be easy to kill the caterpillars.
The next phase when it is going to be relatively easy to kill them is when they turn into moths. And they actually make it easy for us! The female gypsy moths are nearly white, and they don't fly. So, they are easy to spot, and kill. The males are brown and do fly, so are not easy to catch or see, and harder to identify as a gypsy moth versus some other native moth.
The gypsy moths are not native to North America, but they have been in our country since the late 1800s!
I went to college in the early 1980's in Massachusetts, and the gypsy moths had taken over the woods! I recall being in campus in June for orientation, and they were everywhere. In fact, they were so dense that you could hear them eating, and their droppings (called frass) sounded like a light rain! Despite the heavy infestation, the trees have survived. And so they will here, especially with a little help from us!