As a home inspector, I routinely inspect for wood destroying insects while I am doing a home inspection. The most destructive wood destroying insect is the termite. If left unchecked in your home long enough, termites can do structural damage. When we inspect for termites we are typically doing a visual inspection. So we are looking for visual clues. Of course we are looking for the live insects. But the more important clues are not the insects themselves.
The first visual clue is to find moisture in the home. In nature, termites live in the ground. They like to feed on wood. So they are typically in the ground or inside a piece of wood. It is easy to find termites out in the woods in an old tree stump or in some other rotted piece of wood. They are attracted to wet wood. So if you have a plumbing leak or other source of water entery in your home, there is a good chance that you will have some wet wood somewhere. The conditions then exist for termites to live in your home.
The second visual clue is to find mud on the surface of a piece of lumber or on the surface of the foundation. Termites bring mud with them when they enter your home. They build mud tunnels or shelter tubes to crawl in. Termites typically are inside their shelter tubes and therefore you typically won't see them running around like an ant or a roach. The shelter tubes can take many shapes. They are often long slender tube-like structures. They are often about 1/4 inch wide and can be several feet long. Because termites are coming in from the ground around your home, they are usually found in the basement or crawlspace where the wood structure is closest to the ground.
So keep your eyes open for wet wood and mud in your basement!