Below is a YouTube-clip with a presentation on how to apply for ESTA and Visa when going to the United States as a musician. The seminar was organized by Export Music Sweden for the Swedish music industry, but the same rules apply for Danes.
Yasmeen Hibrawi and Mårten Sandmark from the US Embassy in Sweden go through the differences between an ESTA and a B1/B2 visa. They also list what a musician can and cannot do when travelling with these permissions in the US and how to apply for other kinds of visas. This should work as a good introduction for anyone looking into going to the US to do business!
More information on what you need for travelling in the US can be found on the website for the US Embassy in Denmark: http://denmark.usembassy.gov/visas.html