I need to explain the scoring system of Tennis to my elderly neighbour.

[Groomsport]

I find it difficult to lay it out simply though i know it myself. Can you help?

[ladybirder]

Too hard to explain when you're not watching it. Show your neighbour this.
http://www.tennistips.org/tennis-scoring.html

[Anngel123]

Server score is always called out first. 15 for first point scored, 15 for second point, 10 for the third point. If they reach 40 all this is called deuce. the server can win from the next point if the score is 40:30. However, if deuce is reached the winner of the next point has "advantage". They then have to win the next point to win the game. If they lose it goes back to deuce.

[New Judge]

Try this:

GAMES

A game is won by the player first reaching four points by two clear points. The points score is called “15”, “30”, “40” and “Game”. "Love" is used to indicate no points and the server’s score is always called first. If the score reaches 40-40 it is called as “Deuce”. The player winning the next point is said to hold “Advantage”. If he goes on to win the following point he is awarded the game (because he has won the game by two clear points). If his opponent wins the next point the score returns to Deuce. This can continue for as long as it takes a player to win two consecutive points.

SETS

A set is won by the player first to reach six games by a margin of two clear games. However if a set score reaches six games all a “Tie Breaker” is played to decide the set (see “Tie Breaker”, below).

TIE BREAKER

If a set reaches six games all a “tie Breaker” is played. To win this a player must reach seven points by two clear points. The points are called simply as “1”, “2”, “3” etc. If the score reaches six all play continues until a two point margin has been achieved. In Tie Breakers the server’s score is not called first as in normal games, but is called followed by the leader’s name (eg Three-Two Bloggs). The winner of the Tie-Breaker wins the set seven games to six.

Matches consist of the best of three or five sets.

Almost all tournaments operate tie breakers in all sets but at Wimbledon tie breakers are not used in the third of a three set match or the fifth of a five set match. In those sets play continues after six all until a two game advantage is achieved. In 2010 the longest ever set in tennis Grand Slam history was played at Wimbledon when John Isner beat Nicolas Mahut 70-68 in the fifth set of their first round match.

[vascop]

//This can continue for as long as it takes a player to win two consecutive points.
//
Should be "until a player wins 2 consecutive points from deuce"