How to make a dwarf start playing an instrument if he does not have any musical skill?

TL;DR: You can't force your citizens to perform a specific form, much less play a specific instrument. I've had dwarves spontaneousely perform new forms they nor anyone else in the fort had experience with, but at the same time they mostly tend to spam the same couple of forms, so no idea what decides what gets played. Note that if an instrument is stationary, rather than hand-held, it needs to be built within the inn/temple bounds to become available for use.

Instruments are tied to music and dance forms. Specific music forms require specific instruments in specific numbers. Dwarves only play instruments that are required by the form they're participating in. If an instrument required by a form being performed is not found, then the participants will "simulate" it.

Instruments that aren't required by any of the music forms being initiated by your citizens or guests will just lay there useless while they play air guitars and motorboat hand trumpets. My tip is to first observe what forms are being performed in your fort and look into their descriptions. Then prioritize making the instruments mentioned therein.

In my forts the citizens seem to always have a couple preferred forms that they repeat ad nauseum. Letting in some foreign guests can liven things up, but then you'll need foreign instruments for those, which you can't produce yourself. You can get those trough trade or by allowing residency for bards who carry one on their person (or by "convincing" them to hand it over), and maybe also through raiding.

Speculations: What decides what forms get initiated in your inn or temple, aside from wether its recreational or religious? Maybe a creature needs to have experience with the form, which they can learn from others by participating, and maybe also by observing, don't know for sure. Then again, I've had my dwarves spontaneously start performing new forms nobody in the fort had experience with (I checked that, but didn't check in the legends viewer if these forms were ones newly created by these dwarves, or just randomly selected from already existing ones tied to my civ).

It's not really likely, but maybe having other instruments lying about gives them a chance of being included in a new form if it happens to be created in your fort, making them less useless outside of being a trade good.