European Union citizens may legally work in Austria although you are supposed to register with the police within five days after arriving in the country. Non-EU nationals can still find work although the process is much more difficult. You would almost always need to speak fluent German and it helps a lot if you have some sort of Austrian sponsorship or an employer who is willing to apply for your work permit. Contact an Austrian embassy (websitewww.austria.org) for more details.
Although most travellers find work in ski resorts in the Tirol region, it is also possible to find work in Salzburg, particularly for German speaking EU nationals.
Pick up a copy of Rolling Pin (websitewww.rollingpin.at) for a good selection of hotel and tourism industry jobs in Austria.