Assuming you are playing doubles, you would stand in the service box diagonal to your partner (on your side of the court).
If you are standing in the right place, the serve will go past you and into the service box in front of you on your opponent's side.
The baseline
When serving a legal serve in tennis, you must stand behind the baseline. The line you must be behind is called the baseline.
the area that you serve into is the same as in singles. The server may stand anywhere in between the center mark and the doubles sideline
It's where you stand when you serve. Behind the baseline in one of the four corners of the court. Best way I can say it.
International Tennis Federation.
The service line in tennis is important because it marks the boundary where the server must stand behind when serving. It impacts the flow of the game by dictating where the serve must be delivered from, influencing the angle and speed of the serve, and setting the stage for the point to begin.
It stands for Women's Tennis Association
Advantage
ATP stands for the Association of Tennis Professionals.
The receiver must stand diagonally opposite to the server. For example, if the server is on the right side (thus serving to the server's left service box), then the receiver must stand to the receiver's right to be diagonally opposite to that of the server.
In tennis doubles, the rules for receiving involve the receiving team standing on the opposite side of the net from the serving team. The receiving team must return the serve before it bounces twice and the players must take turns hitting the ball. The receiving team can stand anywhere on their side of the court to return the serve.
'Des tennis' are most probably 'des (chaussures de) tennis' which are tennis shoes in English. That could also stand for 'des (terrains de) tennis', which are tennis courts.