What should I do about unintentionally breaking glass cups in my youth, given that I do not know their owner now?

What you did during your childhood carries no sin, for the Prophet, peace and blessings be upon him, said: "The pen has been lifted from three: ...and from the child until he reaches puberty." However, this does not waive the liability, because liability for damaged goods does not require legal responsibility (taklif). So, as long as you do not know the owner of the cups, you may give charity equivalent to the value of the cups on her behalf.