Do is used for a recreational activity or a non-team sport that does not use a ball:
- All classes do gymnastics at school.
- Sophie does yoga with a group of friends.
Play is used with ball sports or competitive games where we play against another person:
- Two people can play a game of tennis.
- You need a team to play football.
Go is used with activities that end -ing. We go somewhere to do something:
- To camp → go camping
We often go camping in the summer.
- To swim → go swimming
Many children like to go swimming.
In British English, you can "do sport". In American English you can "play sports".
A typical mistake Spanish speakers make is using the verb practise for sports:
I love practising sport. This should be: I love sport.
I usually practise sport every evening. This should be: I usually do sport every evening.
However, in American English you can use the verb practise or practice (as it is spelt there) to mean "to train": The team is practicing for tomorrow's competition.