You can say "play" for any musical instrument.
Less-common but specific verbs are:
- pluck/strum the guitar
- beat the drum(s)
- bow on the violin
"Blow on the clarinet" suggests that the payer is either very bad or very noisy. However, "blow" is fine for brass instruments and the saxophone. You would never say "pluck" for harpsichord, even though that is how the instrument works. The player actually uses a keyboard; "pluck" suggests the musician is reaching inside the harpsichord and touching the strings directly.
I wonder if there's a specific verb for playing the theremin...