This U.K. promotional video for a soundproofing company shows samples of some of their soundproofing products, which are similar to those in the USA. They also talk about some of their methodologies, though not in detail.
But just looking at the products might give you some ideas. Note the example of the sheds near the end. It would have been nice to know what they used in the "60% soundproofed" shed (it looked like mass-loaded vinyl and a Homasote-like product), as well as the "100%" !!