It takes place after you arrange the third date. (Unless you get married after the first date, which mainly happens in Vegas and rarely lasts more than a week.) Notice that I said arrange the third date. Because once it is set, the odds are very high that you are going to take the courtship further.
This is not a universal rule, but generally true. I can remember one time that I actually made it to the fourth date before I was rejected, and by email no less. But that is likely because I was paying for every meal, and her appetite superceded her compassion. It happens.
Here's how the dynamic went for me. The first date was typically the weeding out process, during which the lady in question would decide if she wanted to see me again. I always allowed for a second date, even if I wasn't overly attracted, because I never ruled out that the attraction might kick in based on personality and chemistry. Or she might be rich.
The second date meant she was interested or wanted to be sure she hadn't misjudged me on the first date because of bad lighting. The third date was the moment I knew we would be seeing each other for a while. This was a far more comfortable experience for me. I felt like I didn't have to work as hard and was starting to become myself. Maybe now we could split a dessert, share something personal, conceive a child.
Okay, that last part really needs to wait for the fourth date.