You swirl the water, slip the egg in, then let the swirl stop itself. Unfortunately, you can really only do 1 egg at a time that way. You let them sit in the water for whatever amount of time that corresponds to how you want your yolk cooked, i.e. runny to fully cooked. I have to look the times up every time because I don't poach eggs very often, but I think it was a little over 3 minutes for my hubs who likes his yolks very runny to about 4 minutes or a little more for mine, which I like jelly like.
When cooking multiple eggs, just gently tip/slide the individual eggs from a container into the shimmering/simmering water and increase cooking time by 15-30 seconds depending on how many you are cooking.
BTW, I use Chef Eric Ripert's blender Hollandaise sauce recipe/technique. Works every time.