How much Teamplay or Honorable Opponent honor must I earn to receive a badge?
There is no hard number known to receive the honor ribbons.
Per the LoL wiki:
Please note that there are currently no specifics given by RiotGames regarding the exact numbers or formulas used in order to award medals and ribbons to honorable summoners, though there are rumors 100 Honor Points are needed for Friendly, Helpful and Teamwork Ribbons and 30 for the Honorable Opponent Ribbon, although it is confirmed to be possible to get the teamwork ribbon without 100 Honor Points.
The Honor Ribbon is not based on the quantity of Honor Points you have.
It is based on the consistency in which you get Honor.
Basically, your honor per game in a certain section is what determines whether or not you get an Honor Badge/Ribbon.
There are a few other variables that screw around with this value; most surround how many times you have played with/against the person honoring you. You will most likely get more out of a stranger honoring you, rather than a regular duo-queue friend. If you want to gain an Honor Badge, avoid 5-man queues.
Having 25 or 100 were just a few of the false beliefs regarding honor when it was first announced.
There is no way to find out how many honor you've had per game so far. On a side note, if you are punished by the Tribunal for wrongdoings, your honor is reset to 0; your honor per game, therefore, is reset to 0 as well.
I hope this helped you!