What exactly is hermeneutics and exegesis? Two terms that get thrown around on this site a lot are 'hermeneutics' and 'exegesis.'  To the layman, what exactly do these terms mean?
Both terms relate to how a person translates the symbols in a document into a meaningful thought.  Depending on how one approaches a given set of symbols, different meanings can be made.

In at least one classic example, consider:


  GODISNOWHERE


As word-based people, we want to insert spaces.  But, do we insert them as:


GOD IS NO WHERE
GOD IS NOW HERE


How you do is based on your perception.

At its most fundamental, hermeneutics attempts to systematize both how people add meaning (Sapir-Whorf, Act-Theory, etc. etc. etc.), and attempts to suggest some basic principles that guide how it should be done.  For example, some commonly agreed upon hermeneutics:


A text can never mean what its intended audience could not have thought it meant.
A text has meaning when the audience hears it, regardless of what the author may have intended.
If there is disagreement about which the original author most likely intended, the more difficult meaning should not be discounted just because it is difficult.
A word is presumed to mean what it would have meant in most contexts, unless otherwise redefined.


And, further things like that.  The question of inspiration also comes up a lot.

Finally, exegesis is a method that one uses to literally "draw meaning out" of a text.  Given a small bit of Scripture, a preacher doing good exegesis will extract the core meanings out of the text, as opposed to writing his particular meaning into a text. (This is often derivisely called eisegesis for 'writing into')

Some activities that typically happen in good exegesis relate to good hermeneutical principles:


Outlining the passage to see the context in which a particular word or verse stands.
Learning about the culture of the intended audience, to understand how they would have understood it.
Researching alternative uses of a given word, to find the commonalities amongst them.


These principles seek towards one aim- arriving at a common consensus on what a verse really is supposed to "mean" regardless of the biases one might have in approaching the text in the first place.