Points go 0, 15, 30, 40. If they're tied at 40, they go to deuce. After a player gets another point, they get advantage. They'll need one more point to win a game (the one that has advantage).
Sets are won when a player reaches 6 games. If the two players are at 5-5 each, the player must either win by 2 (7-5), or by tie breaker (when each players are at 6-6 in the set).
Tie breakers are done in a points system. One player serves and play for the point. They then switch serves and alternate serving two each at a time. First to 7 wins. Just like the set, if both players are at 5-5 they much win by two to take the set. It can be 7-5 or 19-17 etc. Just as long as they win by two. Tie breakers are and used in every tournament including the grandslams. One exception. If they are playing in a grandslam, a tie breaker is not used for the 5th set (it is used 1-4 sets). The way they can win is winning normally (6-2, 7-5, etc) or by set rules; win by two by playing games, not points.
The Isner Mahut match is in a grandslam tournament so tie breakers are not used for the 5th set. Each of those 59-59 are games (playing with the 0, 15, 30, 40 system). The match will end when one wins by 2.