There are two types of handicapping systems used in tennis - one Play-based and the other Point-based. The play based handicapping makes it easier or harder for one of the players / sides to win a point by changing the dynamics of the game. The points based system gives or takes away points so that unequally balanced players have to win different numbers of points to win a game. If needed, you can use both at the same time.
Play-based handicaps
Advantages (given to weaker player)
Can hit the ball after a double bounce
Can hit the ball into the tramlines
Disadvantages (imposed on stronger player)
only allowed one serve attempt, not two.
You can make up other ideas too here. Use as many advantages / disadvantages as you need to even things up.
Points based handicaps
Players are given a Receive or Owe handicap R-30, R-15, Scratch, O-15, O-30, O-40. (Sometimes notated as +30, +15, 0, -15, -30, -40)
Receive (R or +), means that the player starts with some extra points already on the scoreboard. Owe (O or -) means that the player will give away some points to their opponents. Scratch (SCR /no letter / 0) which means that the player will treat their score as if there was no handicap.
So, if a +15 was playing a -30, you would start each game at +15, -30 - ie. the stronger player would have to win 3 points to get to 15 all. (When handicaps start off on the odd side, it is a good idea to start the game on the Advantage side so that you would always play a deuce as normal - if you get there!). If a +15 was playing a +30, there would be some cancelling out, so the game would start at 0, +15.
More elaborate systems evolve from this where you can give different points on alternative games. Fuller details here for those interested: guide-to-handicap-scoring http://www.brookfieldtennis.com