How we cite our quotes:
[Telemachos] saw Athene and went straight to the forecourt, the heart within him scandalized that a guest should still be standing at the doors. He stood beside her and took her by the right hand, and relieved her of the bronze spear, and spoke to her and addressed her in winged words: 'Welcome, stranger. You shall be entertained as a guest among us. Afterward, when you have tasted dinner, you shall tell us what your need is.' […] [A]nd he led her and seated her in a chair, with a cloth to sit on, the chair splendid and elaborate. For her feet there was a footstool. For himself, he drew a painted bench next her, apart from the others, the suitors, for fear the guest, made uneasy by the uproar, might lose his appetite there among overbearing people […]. (1.118-124, 130-134)
Telemachus knows how to treat a guest right: he welcomes her graciously, gives her a chair away from the suitors, and even brings her a stool for her feet. No wonder Athene decides to help him. (We have to say, knowing that your guest might at any point be a god is pretty good motivation to treat people well.)
(Menelaos:) 'Surely we two have eaten much hospitality from other men before we came back here. May Zeus only make an end of such misery hereafter. Unharness the strangers' horses then, and bring the men here to be feasted.' (4.33-36)
Menelaos gives us some insight into why the rules of hospitality are in place: he treats his guests well, because hosts once treated him well. Gee, it's nice when things work like they're supposed to.
(Nausikaa:) 'But now, since it is our land and our city that you have come to, you shall not lack for clothing nor anything else, of those gifts which should befall the unhappy suppliant on his arrival.' (6.191-193)
The Phaiakians treat Odysseus right, not just because they're generally nice people, but because it makes them look good. If you have enough food and clothing to give away, then you and your people must be doing pretty well for yourselves. See? Everyone wins.