Greece offers a good choice of properties for sale even in the more populated areas such as Athens (the cheapest properties are to be found in the rural areas of the mainland). Generally it’s best to work through an estate agent.
Once you’ve decided on a property a deposit of 10% (sometimes more) will be required from you and a sales agreement will be signed setting out price details and a due completion date, which varies but can be done in under a month. The balance of the purchase price is payable on signing the purchase deed before a Greek notary. The notary will make legal checks on the property which will cost you around 1-2% of the property value to do this. The assistance of a lawyer will make your life much easier: they will act on your behalf in payment of any local taxes (about 0.25% of the property's declared value annually) and register the property with the Land Registry (Land registry fees should be about 0.3% of the assessed value plus a small sum for stamp duties and certificates). Lawyers’ fees usually amount to 1% of the property value. Tax is charged on property purchase by the Greek government at a rate of 11-13%. Real Estate agent's fees are usually paid by the vendor.
Note that interest rates in Greece are very high on mortgages and in any case you will probably find it more advantageous to arrange a mortgage outside of Greece. Local mortgages usually provide up to 90% of the property value and are repayable between 5 and 30 years.
Generally locals react well to foreign property buyers and there is none of resentment that can be felt in other parts of the world.