Complex sentences have one independent clause and one (or more) dependent clause(s). The reason we have complex sentences is to put two similar ideas into one sentence. Usually, the more important of the two ideas takes its place in the independent clause, and the supporting, or contradictory, idea lives in the dependent clause.

There are three kinds of dependent clause:

adverb clause – tells us the where when, why and how the action was done. You can spot an adverb clause when there is a subordinator like: when, while, because, although, if, so or that. An adverb clause can come before or after the independent clause.
adjective clause – describes a noun or pronoun and begins with a relative pronoun like: who, whom, which, whose, that, or a relative adverb like: where or when. The adjective clause always follows the noun or pronoun it describes.
noun clause – begins with a wh- question, that, whether and sometimes if. The noun clause can be part of an independent clause, taking the role of the subject or the object.

Punctuating a complex sentence is also pretty easy. If the dependent clause comes before the independent clause, then you need a comma to separate the clauses. If the dependent clause comes after the independent, then you need no comma.