Nationals of EU countries, Switzerland, Norway and Iceland may work freely in the Republic of Cyprus. If you are offered a contract, your employer will normally steer you through any bureaucracy.
Virtually everyone else is supposed to obtain a work permit, and if they plan to stay more than 90 days, a residence visa. These procedures are well-nigh impossible unless you have a job contract lined up before you begin.
This type of work is a more obvious option in Northern Cyprus, where English is not as widely spoken. There is competition, however, and language-teaching qualifications are a big help, namely a TEFL qualification.
Information on possible teaching work – in a school or as a private tutor – can be found in universities, foreign-language bookshops and language schools. Many have noticeboards listing opportunities or where you can place your own advert.
Summer work at the main coastal resorts is a possibility, especially if you arrive early in the season and are prepared to stay a while. Check any local press in foreign languages, which will normally list ads for waiters, nannies, chefs, babysitters, cleaners and the like.
It is possible to stumble upon work on yachts and cruisers, though it will usually be unpaid. Ask around at the various harbours.