Housing in Cyprus: renting
If you're thinking of living in Cyprus for just a year or two, it's probably best value to rent a property. Even if you're coming long-term and plan to buy, it may well be worthwhile taking out a short-term rental agreement on somewhere fairly central in the area you plan to live in. This gives you a chance to get to know the region, to chat to locals who may advise you, and to explore the different estate agencies.
Finding property to rent for a year or two is fairly easy, and usually rather less expensive than in most of Europe. Property in Cyprus is traditionally owned by women, and passed down to daughters as dowry; hence there are plenty of houses and flats waiting for young girls to claim their inheritance. Long-term rentals can be more difficult, depending on your requirements. Prices vary by area as well as by kind of house, and also - since it's Cyprus - on who you know.
If you take out a rental agreement, make sure you have a written contract. It may be possible to pay a fairly low rent, if you agree to take care of all decorative maintenance of the house; but you need to determine who will be responsible for more major items such as a leaking roof or a faulty toilet. Each landlord or landlady will have a different idea as to what is acceptable.
Buying a house in Cyprus
Buying property is possible, although non-Cypriots need written permission to do so. This is generally granted without problems. Make sure you find a good lawyer if you are buying a house in Cyprus. If you use an estate agent, they may try to convince you that you don't need a lawyer, or that you can use their own one. This is a bad idea. Surveys are not generally done so you may also need to find or employ a builder to advice you on the state of a house you would like to buy.
Some people buy land and then have a house built to their specificiations; this may be the most inexpensive and satisfying solution, but be prepared for a long wait, since time schedules in Cyprus can be more Middle Eastern than European.
For some ideas of prices in various places around the island, you can explore the BuySellCyprus site.