How do fairies become indebted to humans?

You loan them a quarter when they need to make a call from a pay phone.

Saving the life of a fairy would do it.

For example, there's the story of when a man saved a leprechaun that had it's beard stuck. He cut off the beard and was able to ask for the leprechaun's gold. Though the leprechaun got angry about his beard and said that the guy didn't deserve the gold and ran away.

There's also the one where the fisherman caught a fairy fish and because he let him go he got to ask for wishes

And the one called The Queen Bee, where the youngest son saves the life of some animals and they repay him by helping him (one assumes they have some fairy in them).

When you know a fairy's name-the fairy is under your command when you know their name.

When you save a fairy's life

When you give them a simple gift in the human world (which is not made out of iron)

When you give them a song-not any rap or hip hop song, something which means something to them.

Reminder: They don't always have to give/do anything back to you unless you make a deal but the fay are cunning and will say certain words which will wiggle themselves out of the bargain. It must be set into stone in front of other members of fey as witnesses.