The Homeric Hymns, though attributed to Homer in antiquity, are anonymous poems probably composed slightly after the Iliad and the Odyssey were. Some may even be from the Hellenistic period. They are written in the same meter and dialect mix as Homer's poems, so it's not too misleading to continue to call them Homeric.
The Hymns — also called προοίμια, proems — were apparently brief invocations to a god the rhapsodes recited before starting in on a larger epic. They start off by naming a god, asking the Muses to aid the poet in singing about the god, followed by a list of the deity's attributes and hang-outs. They end with a plea for the god for help, often ending with a line saying "and now I'll sing another song."
Here's the shortest, number 13, to Demeter:
Δήμητρ’ ἠΰκομον σεμνὴν θεὰν ἄρχομ’ ἀείδειν,
αὐτὴν καὶ κούρην, περικαλλέα Περσεφόνειαν.
χαῖρε θεὰ καὶ τήνδε σάου πόλιν, ἄρχε δ’ ἀοιδῆς.
I begin to sing of Demeter with the beautiful hair, august goddess,
her and her daughter, the very beautiful Persephone.
Goddess, rejoice, preserve this city, and begin the song.
Most of the shorter hymns are in the 5-15 line range, but it appears that the hymn could be elaborated out to greater length. A few are quite long, such as number 2, also to Demeter, which has 495 lines. The ending formula saying that another song is coming is still in place, but it may be that this is simply a stylistc element of a form that had acquired a life of its own.