The word “classic” can be either an adjective or a noun. There’s a beautiful and witty quote by Mark Twain explaining quite well what the noun means:
A “classic” is a book/song/film or any other piece of art which is considered to have set a high quality standard in its respective genre. Much less frequently, it is used also for the author of such a work. Similarly, “a classic thing” is something that is in some way typical for its class (e.g. “a classic mistake”).
“Classical” means “traditional” or “being present for a long time”. In science, for example, a “classical theory” is a theory that has well established itself as a useful scientific theory, although it often contrasts with another “modern theory” which is able explain more than the classical one. “Classical music” refers to well established music genres of the past centuries.
A classic example of the distinction between “classic” and “classical” is “a classic/al example”. “A classical example” is not strictly speaking wrong; it means an example that has been used for a long time. But what you mean 99% of the time is “a classic example” which is the same as “a typical example”. See the following chart of usage of the two phrases in English literature: