Learn Icelandic: Ég gerði þér lítinn greiða í gær.

This is the dative of advantage (dativus commodi). While the direct object of what you are doing (greiða) is in the accusative case, the person who benefits from the favor is put in the dative case. So, þér natively expresses "for you" here without needing a preposition.

Why is the adjective lítinn used instead of lítill or lítið?

It has to agree with the noun it modifies, greiða (favor). The word greiði is a masculine noun, and since it is the direct object of the verb gera, it takes the accusative form greiða. Therefore, the adjective must also take the masculine accusative singular form, which is lítinn.

Could I use a preposition and say ég gerði lítinn greiða fyrir þig?

While English speakers naturally want to translate "for you" literally with fyrir þig, it sounds clunky and unnatural in this context. Icelandic strongly prefers using the dative pronoun (þér) right after the verb to express doing something for someone's benefit.

I remember gera usually translates to "to make". Is gera greiða a fixed phrase?