Types of Definition
 
Dictionary or formal definition
This is the default. Use this only as a beginning to help you see what terms might be used to define a concept. To simply go only to Webster's for your definition is to give an over-simplified explanation to a complex term.  

Extended definition
Frequently used when the term or concept is complicated. This means you write a paragraph or page or paper (or even book!) to make your concept known to your audience. Our assignment is in effect an example of this method. Sojourner Truth's famous speech, "Ain't I a Woman?" demonstrates this method powerfully.
Historical or Etymological definition
This uses the history or root of a word to further explain a word. How a word has been used through history can also be instructive. Words such as "silly" or "pity" or "luxury" have changed over the years to mean something new today--and often quite different--than what the words used to mean long ago. The words "education" or "enthusiasm," for examples, picked apart etymologically can be surprisingly instructive.
Definition by example
Perhaps the easiest way to define, and frequently the most helpful, is to give an example of how the term is used. For longer definitions, an example or two frequently can make a complex or abstract concept understandable.
Definition by negation
To explain something by showing us what it is not is to define by negation. Frequently, this tactic can be used to shatter a stereotype or to undercut conventional wisdom.

Definition by synonym
Difficult or abstract terms can be made understandable by simply throwing other words at them. I said our paper assignment was an expository paper, but that word "expository" may not be familiar. So I defined by synonym, saying that this was also called an "information" paper, where the writer passes information to an audience. You probably had no trouble recognizing that synonym, and now in your brain you can associate the two words so that when you hear one, you know it also refers to the other.

Definition by analogy
This method assumes a concept is difficult to define and so uses something much less complicated and much more understandable as a comparison to shed light on the difficult term. The thinking is that if your readers knows the simpler concept, they can infer the meaning of the more complicated concept.
Stipulative definition
To stipulate is to define a term by certain criteria. When you use a stipulative definition, you will hear language such as "What I mean by this term is..." or "For the purposes of our discussion, this term means..." This confines the discussion about a term to a limited scope of possibilities. If the audience agrees, then it doesn't matter if the term has many other meanings--you are just agreeing to accept a certain definition for your discussion.

Here's a very personal, stipulative set of definitions, for example.