The prime minister was proposed by the party leaders but can only be  appointed by the president of democracy in this case Carolos Papoulias, then the parliament has to provide a confidence vote to the new PM and to the new government. If you want you can read the part on the Greek constitution (there's an on line edition if you google it in English too I think) where it is explained in details how a PM is appointed. But the general idea is that after elections the party that comes first in votes,  proposes a P,M the president appoints him and the parliament has to give the confidence vote to the new PM and the government  . In this case were we have a coalition government consisting of three parties, they all came to the conclusion of proposing mr Papademos and then the same procedure takes place.