Do
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
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
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.
See more at:
http://pt.slideshare.net/Alicekolos/sports-and-games-6th-form
https://www.facebook.com/MEIT-international-English-teacher-399314250236538/