Where did Stannis get his naval command experience prior to the battle off Fair Isle? There was no Targaryen fleet to oppose him when he took Dragonstone, and there was no great naval threat in the years between Robert’s and the Greyjoy Rebellion for him to hone his skills, afaik. Do Baratheon sons receive some kind of basic naval training, given their proximity to the sea?

There was a Targaryen fleet opposing him, it just got wrecked in the storm. Regardless, overseeing the construction of an entire fleet and then coordinating that fleet on a successful amphibious attack in those circumstances is a hell of an entry-level work experience gig. 

Afterwards, Stannis was the Master of Ships and Lord of Dragonstone, and we know from ADWD that he was extremely active in fighting pirates, which would give him lots of smaller-scale experience. And of course, Stannis being Stannis, odds are that he read and memorized manuals of naval warfare as due diligence for his new job.