In English you normally play a game but do a lot of / a bit of sport:
In the winter I do quite a lot of skiing; in the summer I play tennis and cricket.
Ball games and equipment
For most ball games you need boots or training shoes (trainers).
For tennis, squash and badminton you need a racket.
For baseball and table tennis you need a bat. For golf you need clubs.
In tennis, volleyball and badminton there is a net across the middle of the court. There is also a net around each goal in football.
Things you can do with a ball
Places and people
The playing area for football, rugby, hockey and cricket is called a pitch; for tennis, volleyball, basketball, squash and badminton it is a court; for golf it is a course.
Note: When you describe the playing area for football and the area around for the crowd (= the people who watch, also called spectators), it is called a stadium, e.g. Wembley Stadium. Players: Some games are played by individuals, others are team games. In a team, one player is the captain, and there is a manager (e.g. in football) or a coach (e.g. in basketball).
Officials: Football, rugby and hockey have a referee but tennis, cricket and baseball have an umpire. In football the referee has a whistle to control the game and two linesmen. In tennis there are line judges to decide if the ball is ‘in’ or ‘out’.