This one is teasing me. I read it somewhere in the mid 1990s, I think, between 1992 and 1998 (somewhere in that middle to high school era). It was in English. The main character was a woman (I think a redhead) from our world who winds up in a fantasy world. One of the first people she meets is a man with a staff (I think also a redhead) who is traveling to an important contest that involves singing (he was chosen and trained for it by his village, I think). He treats her with the patronizing air one might expect from a medieval fantasy society. She sets him in his place, I believe toppling him with a self defense throw at one point to show him she could take care of herself. She winds up traveling with him, I think also with a bunch of homeless kids (called the "Littles"?) and enters the contest with him.
She winds up winning, I think with "Simple Gifts" and gets a magic cup as her prize. She uses said cup as a cup, including filling it with the local intoxicating beverage, which I remember being describing as dark and thick. Drinking it from the magic cup results in her having a vivid dream, or maybe a hallucination. At the time, it reminded me of the scenes in Labyrinth and in Legend where characters semi-hallucinate a dancing scene, but I don't remember if it actually involved dancing. When she wakes up the next morning, she finds out her male companion has attached himself to her, essentially to protect the cup more than her, as he thinks she isn't taking this seriously (and really, she isn't). Also, the "Littles" get in trouble with the law for sleeping together. The female protagonist insists that they all sleep in a big pile together and it's totally innocent, but it's then clarified that they were caught having sex.
I'm pretty sure this one will come to me eventually, but it's just not coalescing in my head, and my Google searches have not done me much good either.