Here is a short explanation of the scoring I think we decided on using:

game scoring: ad (advantage) scoring--first to 4 points, have to win by a margin of 2
If you want to use the right language:
0 = love
1 = 15
2 = 30
3 = 40
The server should say the score before each serve, and they always say their score first. If both players both get 40 (3 points), it's called deuce, and you keep playing until one player wins two points in a row. In that situation, the second point, served on the left side of the court, is called ad-in if the server won the deuce point, and ad-out if the receiver won it.
set scoring: first to 6 games, have to win by margin of two
If both players win 6 games, you play a 12-point tie-breaker:
First to 7 by a margin of two. The next server in rotation (in singles, whoever didn't serve last) serves the first point, and the other player serves the next 2. From then on, the serve switches every two points, so each server should serve their first point on the ad side (left side) and the second on the deuce side (right side).
Especially if playing outside (and inside, if you want) you are supposed to switch ends of the court on odd set scores, except for after the first game, and after every 6 points in tie-breakers.
match scoring: best 2 out of 3, if one player wins the first 2 sets, you don't play a third
for more details, see http://en.wikipedia.org/wiki/Tennis_score
as we said, rules and language don't matter that much, as long as both players agree on how to determine who wins.

courtesy of mwilder1