My porcelain tooth broke off at the gum line. How can I fix that?

Your porcelain crown that broke at the gum line needs to be reviewed by a dentist.  Has it had root canal prior?  If not it will need it now.  Was there a post involved if it had root canal previously?  Your dentist can assist after an xray.  Lastly if the crown still fits the margins and you need root canal...following a post you may be able to have the crown retro-fitted to the tooth.  If the margins do not match you may need a new crown as well.  See a dentist immediately

If the tooth and crown broke off at the gumline, there is probably little that can be done to save it. Having it removed and an implant ideally or a bridge done to replace the missing tooth would seem to be indicated.