I started dating someone new, but haven't talked to my girlfriend about it

I recently (today) started dating someone but I've been dating my gf for 9 months how do I discuss polyamory with her?

You need to discuss polyamory with your current partner BEFORE getting into a new dating relationship! This is not a situation where you just inform your partner that you’re now dating someone else. This is a situation where you need all parties to be fully consenting to the new polyamorous arrangement. Dating someone without first “discussing” it with your partner is called cheating.

You need to move quickly to resolve this. Let your new partner know that your other partner was not informed and on board, and that you need to fix that. Tell your girlfriend what’s going on. You need to provide her with all the information: that you started dating someone new, realized that’s not how polyamory works, and now need to let her know the situation.

However she chooses to act on the information you provide her is up to her. It’s entirely possible that your girlfriend will feel blindsided, hurt, and betrayed by how quickly and secretly this moved. That’s totally reasonable, and you’ll need to graciously accept the consequences of your choices. Avoiding talking about those choices will not protect you from those consequences.