Hungary is very accessible to most people of Western nations, and citizens of the EU, Canada, USA and others do not require a visa for up to 90 days.
While Hungary is part of the European Union, they are not part of the Schengen Convention and therefore when you cross the border from Austria for example, you will have to produce your passport to be stamped (EU citizens must have their ID cards). You are able to remain in Hungary for 90 days and may extend this up to 180 days. Contact your nearest Hungarian consulate for more information.
Studying and working in Hungary however requires the appropriate visa. If you plan on working in Hungary you generally need to apply for this BEFORE you leave your home country - you cannot apply from within Hungary. You may also need a college or university diploma translated in Hungarian as well as confirmation from a company in Hungary that you will have a job.