0. Update your iPhone to iOS 9.3.
1. Settings → Notes → Password → Enable Touch ID and enter a password to protect your notes.
2. To password (or Touch ID) protect a note, you'll need to click on the Share icon when the note is open
You must manually lock or unlock a note. It seems, though, that unlocking a single note will unlock all of the notes (or at least it appears that unlocking a single note unlocks all the notes that were locked with the same password). I'll post updates, here, if I discover anything new.