For each player, if they win a point, the scores go - 15, 30, 40 - and the same for the opposing player so you can have any combination of those points (eg 15-0, 15-15, 30-15 etc.)
If a player is on 40 (i.e. won 3 points) and the opposing player has not won more than 2 points (so is on no more than 30), and the first player wins the point, they win the game.
If both players get to 40 (so effectively 40-40), this is called 'deuce' and a player needs to win 2 more points to win the game. Once they are at 'deuce' the player who wins the next point is 'advantage X' - if they then win the next point, they win the game. However, if they lose the next point, it reverts back to 'deuce'.
In terms of games, it is the first player to 6 who wins the set - as long as there is at least a 2-game margin in it - so 6-1, 6-2, 6-3 or 6-4. A player can also win a set 7-5 - but if it gets to 6-6, they have to play a tie-break which is simply the first one to 7 points, again, they have to have a 2-point margin (so no more than 7-5) - if a player reaches 7 and the other player has 6, they carry on playing the tiebreak until one player is 2 points ahead.
With Wimbledon, it is the first to 3 sets who wins the match.
Now, it seems simple in my head (but I LOVE tennis so it is just instinct to me) - but very complicated to type out so sorry if it doesn't make any sense
In each match, the scores go up 15, 30, 40, win. Unless it gets to 40:40 which is Deuce. From there, one of them has to get two points in a row - they go to "Advantage A" then A wins if they get the next point, otherwise it goes back to Deuce.
They have to win 6 matches to win the set.
At Wimbledon, men (singles and doubles) play up to 5 sets, but women and mixed doubles play 3 at most.
Oh and there are tiebreaks...
If they get to 6 matches all in a set, they will play a tiebreaker, except at Wimbledon in the final set they don't....