Any stones of the opponent that get caught between two of your stones by a newly set stone are flipped, i.e., they change color. You may only set a piece if doing so will flip at least one other piece. Otherwise, you have to pass, and it's again your opponent's turn. The game ends when either the board is full, or neither player can make a move. At that moment, the player who has the most pieces of his color has won.
Draws are possible.
A very good introduction to the game of Othello can be found on Colin Springer 's Othello Pages. Well, I never tried it, but I don't see a reason why you couldn't. You'll need to grab the files Othello.jar and table.code.gz . See the license for information on how to get the applet and on what you are allowed to do and what not. No, I can't.