Normally the knob on the towball would stay latched open and you just shove it in, however I had a bit of trouble with ours after my wife removed it, she managed to push the knob in and turn it part way and remove the towball before the knob latched in the open position, against the spring.
This meant some faffing was required, I think I had to hold in one of sprung parts on the mechanism (making it think its still attached to the car) before I could push the knob in and turn it to the point where it latches and you can let go of the knob without it springing back.
Once the knob is latched open you then just shove it in and it’ll clunk in reassuringly.
(edit – slightly confused, I don’t think you would ever turn the knob to the green position, you would turn it into the red position to remove, and when the ball is correctly inserted it will spring back to the green, at which point you can lock the knob with the key.)