Need help with the notation in Beethovens Pathetique 2nd movement. Bars 20 and 21.How are these played? What notes are played forthe ornamentation.
You are going to play something more or less like this - it's called a "turn":
I say "more or less" because ornaments are meant to be tackled rather freely within the duration they have to fill, so these specific durations may be taken with a grain of salt. The up-and-down of the S-curve tells you to go up a step, return, then go down a step and return. Accidentals above or below apply the upper or lower auxiliary note respectively.
Turns can be placed in two places: between a note and its successor, or directly above the note...
... which produces something like this...
...(bearing in mind what I said about fairly free execution within the duration of the note - these last two examples are from Wikimedia). The difference is that the turn between the notes starts on the main note; the turn above the note starts on the upper auxiliary.
Von Bülow's "instructive edition" (first published 1875, https://imslp.org/wiki/Special:ImagefromIndex/30364/torat) suggests playing the turns a bit faster than @Patrx2, but the general principle is the same.