A complex sentence is made up of two clauses: one independent clause (a simple sentence) which can stand on its own, and one dependent clause that would simply be a fragment if left alone. The dependent clause also contains the subordinating conjunction (the word which ties the two clauses together). Subordinating conjunctions are words such as “because,” “although,” “if,” “when,” “unless,” etc. Are you still awake?
A common error occurs with this type of sentence though because there seems to be confusion on where exactly to pencil in the pesky little comma. The rule is simple:

If the dependent clause comes first in the sentence, there must be a comma. (Why, there’s a good example right there.)
There is no need for a comma when the dependent clause ends the sentence. (Again, a great example.)
(The dependent clauses are illustrated in italics.)
One of the trickiest situations seems to be the use of “because,” but the same rule applies. Folks tend to pause before using that word in a sentence.

• Because Hammock is a cool place to work, many people are sad that their paychecks don’t come from here.
• Many people are sad that their paychecks don’t come from Hammock because it is a cool place to work.

Whether your words are being published in a magazine or sent in an e-mail to your mother, using complex sentences can add great variety to your writing. Once you have the rule down (Dependent clause first, use a comma. Dependent clause last, no comma needed.) then complex sentences aren’t quite so complex.