Hi I'm currently in the EU applying for internships/full time positions in the US. In most applications I have to state whether or not I'm "legally authorized to work in the US". I'm not sure why I would not be, but I don't know exactly what "authorized" means in that sense. Is it asking if I already have a visa? If I don't yet have a visa, is it relatively easy/fast to get one in time for the summer and if so is it ok to answer "yes" even though currently I am probably not authorized because I don't yet have a visa? Or do I not need one at all being from the EU and staying only a couple months or so?
You cannot work legally in the US without a type of Visa that permits you to work. It is not a fast process, and it depends on your country, your profession, how long you are staying, etc.
I suggest that you go to the US Embassy / Consulate in your country for information. They have web sites:. http://www.usembassy.gov/

http://www.schengenvisainfo.com /
Thanks. So every European who applies for an internship in the US has to get a visa first, even though they may not need it?
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You do need a visa to work to work in the US.

You may be allowed in without a visa as a holidaymaker/visitor, but you can't then work legally.