Go is a game of territory. Two players alternate turns, each placing one stone on the board in an attempt to surround as much territory as possible. Groups of stones can be captured when they are completely surrounded by enemy stones. It is important to keep in mind, however, that the game is about surrounding territory, not capturing prisoners.
Learning from GoEdit
Lots of people see lots of different things in go. Some see a war game where each stone is a little soldier, and the best general wins. Others see a more peaceful trading game, where each player makes compromises on what part of the board they want. I have heard that one of the more traditional views was that the board represented the earth, and the black and white stones are night and day fighting over the earth for all the days of the year (361~=365). Some people even view the board as economics, where stones are businesses and the board is unreached markets.
These variations in what people see also determine what they can learn from it. From being a better general, a better negotiator, to being more at peace with the world.
There are three rank scales. The low scale is called "kyu". Kyu ranking numbers decrease with increased ability, so 30 kyu (sometimes abbreviated as 30k) is the weakest and 1k ("first kyu") is the strongest. The middle scale are the amateur dan levels starting at 1d and going to 7d. The high scale are "professional dan" rankings. 1 dan ("first dan") is the rank above 1 kyu (however, a professional 1 dan is typically strong enough to be a rank up from an amateur 7 dan), then 2 dan, and so forth up to 9 dan. Professional ranks also follow the dan scale, but they are denoted 1p-9p to indicate that they are separate from amateur ranks. In Korea "gup" is used in place of kyu. The scale is 18 gup to 1 gup.
Ranking is simply a convenient way to set handicap. This allows players of different strength to have an interesting game despite their disparity in skill. A general guideline is that the player taking black (the weaker player) receives one handicap stone per difference in rank with the white (stronger) player. Placing handicap stones is black's first move.
Several ranking tests are available online; one such test is on this site.