t depends on the activity. (These are usage examples--I don't do all these things!)
Sports: "play."
I play golf. I play tennis. I play chess. I play video games.
Exercise: just use the verb "to exercise," or use "take."
I take exercise. (But that's a little old-fashioned or perhaps British. I personally DON't say that).
I exercise.
I exercise twice a day.
I exercise at the gym.
Special use: DO exerciseS meaning a specific exercise.
My physical therapist has me do exercises for my knee.
To maintain my fitness, I do exercises like push-ups and sit-ups.
To do a SET of exercises for fitness and muscle tone is called "working out," or "a workout."
He looks like he's in good shape, I bet he works out.
I work out every day. On a business trip, I always choose a hotel with an exercise room.