Play
The names of sports that do not describe the particular "action" of the
sport (in other words, the name of the sport does is not also the verb
of that sport), take "play."
play tennis
play soccer/football
play basketball
play lacrosse
play rugby
Note, in these sports, there is a sense of competitiveness, that at the
end of the day, there will be a winner and a loser in the match and/or
game.
Go
Sports verbs where the actual activity is the verb take "go" with the -ing (gerund) form of the verb.
swim / go swimming
surf / go surfing
sail / go sailing
I am going fishing.
They went hunting.
The boys like to go hiking in the mountains.
Note, in general, these are "singular" sports, although they can be competitive, but not so much on a team level.
Do.
In my experience, do is used more for particular recreational
activities, especilly those of a singular nature, and not so much for
sports.
I do (practice) yoga.
Mr. Smith does crossword puzzles.
One notable exception is golf, which can use several forms.
Mr. Jones golfs every Friday afternoon.
My husband plays golf when the weather is nice. In fact, he is going golfing with his friends this weekend.
