Play is used with sports that have teams, rules and competitions: badminton, baseball, football, golf, rugby and tennis etc.
- I often play tennis.
- Do you play poker?
- I don't like playing computer games.
- You play golf
Do is used for recreational activities and a non team sport that does not use a ball: Aerobics, athletics, gymnastics, judo, karate and yoga .
- I do a crossword puzzle in my free time.
- They do gimnastics.
- Sarah does yoga with some of her friends.
Go is used with activities and sports that end in -ing. The verb go here implies that we go somewhere to practice this sport: go swimming, dancing, jogging, running, hiking, riding, swimming, cycling, climbing etc.
- Are you going skiing this winter?
- I go swimming twice a week.
- They go fishing.