“Dating” means youre going on dates. You are actively getting out there and meeting people and spending time with them. “Dating someone” means youre seeing somebody specific, with purpose and on a regular basis. Youre spending time with a person (or persons) in hopes of finding a committed relationship.

Do you count the first month of dating?

If youre “dating” and not currently in a long-term committed relationship, the answer is generally “Oh we met on this day/month” or “Weve been dating since this day/month”. Once youre official, whatever official means to you, you can use either when you met or when you became an official item.