What are the basics and options of brining meat, for example chicken?
I suggest reading this Cook's Illustrated - The Basics of Brining (PDF) article. I use their basic brine all the time.

This article taught me two cool things I didn't know about brining.


Adjust the amount of sugar &amp; salt downward for high heat applications.

Decreasing the amount of sugar ensures that the exterior of the meat doesn't burn. Prior     to learning this I had a few "issues" with this mishap

Air drying chicken and turkey in the fridge after brining allows the skin to dry out, enabling it to crisp nicely when cooked.


If you aren't familiar with Cook's Illustrated, they bill themselves as America's Test Kitchen. They will take a recipe and beat on it with dozens or more variations tweaking and analyzing it as they go, until they come up with the "ideal" something or other. In this case, it's brining. 

With this as a base you have a lot of opportunity for experimentation. I usually add very hearty aromatic spices to mine. Some possible additions and substitutions:


Whole peppercorns
Ancho chiles
Whole Allspice
Cinnamon
Cloves
Candied Ginger
Brown sugar in place of sugar
Substituting some vegetable stock for water **Use the lowest sodium stock possible, and adjust salt accordingly. I don't have a hard-and-fast rule here, but I tend to go with about 20% less salt than the "basic", more or less.


Another thing addressed by this article is what meats should and shouldn't be brined. The short version is lean mild meats are suitable for brining, fatty meats or those often cooked rare/med-rare do not benefit.

Suitable


Cornish Hen
Chicken
Turkey
Pork
Some seafood

Whole side of salmon (grill roasted or smoked)
Shrimp



Unsuitable


Beef
Lamb
Goose
Duck