I come from EU. My question is: can I legally travel to US and work there even if I am a minor? If yes, what are the requirements and what are the steps I need to take?
Regulations pertaining to employment for people without permanent resident status can be found here. A minor can travel to the US, but may require a visa: EU nationals are eligible for the visa waiver program, but that precludes for-credit study or employment, and if you're been in certain countries (Iran, Iraq, Libya, Somalia, Sudan, Syria, or Yemen) since March 1, 2011 then you're not eligible.
Here is a situation where I think it is impossible: you get a visitor's visa to stay a month as a tourist, and pick up a few hours working at a local grocery store. It is however possible for an prospective employer to petition (in advance) for you to be a temporary worker.