Randy is right - it could get quite complex, and depend on the context - but very broadly, to do something is to perform an action (which may, or may not result in the production of something). To make has the clear connotation of producing something although the something doesn't have to be a tangible object e.g. to make (cook) a cake; to make a noise; to make a fuss, to make a fool of yourself. If you are looking for clarification of which to use in a particular situation, post the sentence and I will be happy to tell you which is correct.

This is like asking the difference between the Spanish verbs hacer and dar. The usage in so many cases is idiomatic that a simple answer is impossible.