European Union citizens can legally work in Austria, though you must register with the police station within five days of arriving in the country, this is a quick and easy process. Non-EU citizens can still find work, though the process is much more difficult. EU citizens can visit Austria without a stay permit or visa. You also don’t need a work permit, although if you stay for longer than three months you will need an ID Card (EWR-Lichtbilausweis), which does include a residence permit.
Most travellers find work in the various ski regions especially in the Tyrol region. However, it is also possible to find work in Salzburg, particularly German speaking EU citizens.
Young people from abroad may work in Austria as an au pair. Au pairs are accepted as part of the host family and integrated into their everyday life.
There is plenty of work available in the tourism industry. Finding a job can be as easy as turning up at a hotel and asking. Seasonal work in the large ski resorts is probably the most likely option.