Ring games: 9 or 10 people sit around a table and play poker for cash. Chips have cash value. The game has no definite start or end. You can join/leave at any time and play for as long as you like.
10 max ring has a maximum of 10 players. Minimum of 2 (obviously).
6 max ring has a maximum of 6 players. Min of 2.
The poker room takes a certain percentage from each pot for profit (rake).

Sit and Goes (SnGs): Start with a certain number of players. Each player is given a number of chips, the same for each person. Game starts. When your chips are gone you are eliminated from the table. Game ends when all but 1 player is eliminated. He is the winner. Usually prizes for 1st, 2nd, 3rd (depending on site, type of SnG etc).
Blinds increace at regular intervals to stimulate play. Blinds increace faster in Turbo SnGs. SnGs are defined by a buy in, for eg, $5.00 + 0.50. The $5s are added to make the prize money, the 0.50 goes to the poker room (rake).

MTTs: Like SnGs but with much more players and numerous tables. There is a specific buy in,which covers prize money and rake (like SnGs) if you loose your chips you are eliminated. Prizes for a certain number of places. Blinds increace at regular intervals.

'$25 No Limit' means the (max) buy in is $25, yes this is the most you can loose if you dont top up your stack or rebuy. The Big Blind is usually (in my limited experience) 1 hundreth of the buy in. So for $25 NL the big bling will be 25 cents. The small blind will be approx. half the big blind, in this case 10 or 12 cents.

You can download most poker software and just watch the games without depositing. I know you can do this with party poker anyway. This may help you.

Also, and I know I might get burned for saying this, but perhaps play some play money. It will help you get used to the format and discover what each game is about. Pay no attention what-so-ever to the style of the players who play play money, their tactics or how they play. Real money is completely different.

Hope this helps.