The easiest way to thicken a sauce is to simply reduce its volume. When boiled, water in the sauce is evaporated. This not only thickens the liquid, but intensifies the flavors and colors too.
A sauce will only reduce if it is simmering or boiling. There must be bubbles popping on the surface. With each popped bubble, water is vaporized. The more surface area you have the more bubbles can pop, and therefore the faster the sauce will reduce. I like to use a big, wide sauté pan. Watch it carefully, because reduction can go quickly.
Thick sauces should be stirred frequently (or constantly, depending on the sauce) to prevent burning.
To judge if your reduction is ready, test it’s thickness on the back of a spoon. Dip the spoon in, then run your finger along the back through the sauce. The trail your finger makes should stay put, and not be filled in quickly with sauce.