Compare to northern Europe accommodation is ridiculously cheap. Of course the prices vary depending on the place and season but still most of the time you'll get a bargain. On most islands it is quite easy to find a place to stay only during high season I'd recommend to book in advance.
Hotels and rooms on the islands
There are countless hotels and pensions in Greece and at this stage they are actually OK. Most of them even have a private bathroom and trust me that's a rather recent development.
The price for a room will mainly depend on three factors: the - lets call it - level of luxury, the time of the year and your ability to bargain. No joke; haggling is still big in Greece. Unless the place is already pretty busy there is always room for negotiation. During high season there isn't much point though.
Greece has an interesting system in place. To protect guest from being ripped off the local authorities check the rooms and put them into categories. They vary from A to E with A being the fanciest. They also determine a maximum price the owner can charge. Then they issue a document that has to be put on display in the room. This way you'll always know what the maximum price for that room is. If they charged you the full price and it is not the highest high season (July / August) you are being ripped off!
There are few single rooms you would normally pay for a double room. It's not a big deal since prices start at 12 Euro. In most places you should be able to get a decent double room for about 20 Euro. Saying that during high season prices can easily go through the roof. Especially places like Santorini, Mykonos or Corfu have a pretty bad reputation for being quite expensive.
Hostels are my favourites. You find hostels on Crete (Iraklio, Rethymno and Plakias), Santorin (Perissa, Thira, Oi), Paros, Rhodes, Ios und Corfu. Prices start from 8 Euro the standards vary. The by far best hostel is in Plakias (Crete). If you only want to see one hostel in Greece, that’s the one to go to.
You don't need to be a member with one exception: the only official youth hostel in Athens. The Greeks didn't want to pay the membership fee for the international hostel organisation so they got kicked out. Good for you.
On most islands with some sort of tourism you'll find a camp site. If there is one camping on the beach is normally forbidden. It actually always is but in some places it is tolerated. Especially in smaller places they don't care too much. Most camp sites are not particularly nice and compare to hostel prices they are also expensive. May be I'm getting to old but I just can't recommend camping in Greece. It's just too hot and dusty in most places and on top most of the time the facilities do not deserve their name.
If you intend to stay longer you can rent an apartment for a pretty low price. A room with private bathroom and some sort of cooking facility should cost no more than 200 Euro a month. Bills are included. You don't normally get a contract. You just pay your rent one month in advance and that’s it. Finding a cheap place however can be time consuming. Best is to inquire with people that already live in the area.
Prices depend on demand. In little villages in the middle of nowhere you'll easily get a room for 100-150 Euros a month, in more touristy areas you'll pay at least 200. If you stay for the winter you can negotiate a discount of 20 – 50 %.
Most of the cheaper rooms won't have a telephone line or heating. On cold days you just use a radiator. Your landlord may charge you for electricity in these cases.
Sometimes you can rent a whole house. Prices start from 350 Euros. They are usually fully furnished.