The pieces fall into place rather well - the ritual doesn't require more than a trivial sacrifice, they think, or at least not the one that looks likely for a first attempt (Professor Quirrel cautions them they may have to spend a while tweaking it). Just a drop of blood from each girl, smeared on a set of runes about transformation and rebirth that Professor Quirrel helps them research.
The incantation they reconstruct from a fragment of a journal is kinda long and also in Old English - translating the entire thing's really difficult, but it's pronounceable, and it does seem to be something about inviting the archetype or spirit of an animal to come and be before you, so you may become it. There's a lot to do, to the point they're both having significant trouble remembering all the steps - at which point Professor Quirrel hums and says he has some (old, somewhat finicky and also very choosy) magical items that can improve recall. Two circlets, both made of silver and fairly plain. One seems braided, with a blue gem set to rest over Ellie's forehead, and an inscription in Old English twining along it. The other's a bit more ornate, with carvings of birds and cats, with a deep red gem over the forehead. The ruby one doesn't seem to work for Ellie at all, but helps Anathema a lot, while the sapphire works rather exceptionally well for them both.
Anathema pours over some astrology charts, tentatively picking a waxing half moon as an auspicious night. Professor Quirrel writes them notes allowing them to be out past curfew, and then, with a few mental rehearsals and preparations, they can begin.
Professor Quirrel notes he'll be observing, in case something goes wrong, but he won't be involved in the ritual itself.