Those ancient languages and English too until it dropped most of its inflected endings had no concept of rhyming since one could not go around changing the endings of words and preserve the meaning of the sentence, so they mostly relied on alliteration to cue them as to what came next. Each stanza in a poem or song in Old English was split in two and the first half was bound to foreshadow the first stressed sound of the second half. To illustrate this idea of alliterative meter in a contemporary example, here’s a passage from American Poet Laurate Richard Wilbur’s Junk:
An axe angles from my neighbour’s ashcan
It is Hell’s handiwork, the wood not hickory.
The flow of the grain not faithfully followed.
The shivered shaft rises from a shellheap
Of plastic playthings and paperplates.
One could imagine our gleemen chanting this opening as easily as one could imagine them performing Beowulf. Although we cannot rule out that ancient and medieval people did not have memories far more expect than ours, having to do without the crutch of a written language, but one can probably safely assume that there was quite a bit of improvisation going on.
Though the poem was painstaking composed and each hung together, if a minstrel forgot a line or a particular passage, a really good showman could recover and reinsert the stumbled line without violating the meter or structure of the story. As Old English did not have a huge vocabulary to draw from (though maybe traveling helped also to keep redundant words in circulation as they traveled from court to court singing the praises of their own lord and sometimes it was handy to have a few different sound options at one’s disposal even if they meant the same thing and it did just sound like a lyric-conceit) and adjectives and attributions were limited, the minstrels often invented so called stock-phrases as colourful metaphors and euphemisms.
When needed, a resourceful performer could add a “fleet-footed,” “rosy-fingered,” “broad-pastures,” etc to substitute for a stray sound. These were not just cliches as the French invaders disdained them as but led to new compound words and concepts that were in common-parlance. The tradition slowly withered away with the advent of writing and nobles (the titles lord and lady were once kenning-words that came about through this method, originally a compound for loaf- guardian and kneader slurred into single syllables, among many other inventions) no longer needed to retain entertainers to spread their good deeds and heroics and transformed into itinerant groups of actors, story-tellers and artists yet but no longer journalists.