Spins cannot occur without stalls. To enter a spin, a pilot would hold the elevator up and let speed bleeds off. This is how you'd approach a stall. Just as the stall starts to develop, apply full rudder; now the world is spinning around you.
Now, how does one enter an inverted spin? How do you stall an aircraft while it is inverted?
When inverted, cut power. As speed bleeds off, gradually move stick forward keep your flight level, the nose will come up quite a bit over the horizon. It is important not to start sinking here as that will prevent the speed coming down low enough. When the stick hits the forward stop, kick in full rudder either way.
Enjoy!
The easiest way to enter is the same as for an upright spin.
Cut engine. Bleed off speed. Keep altitude by pulling gradually. When buffeting indicates approaching stall, push stick decisively forward to mechanical stop and rudder pedals to one side. Same as you would enter a negative snap roll.
This is a clean and gentle entry, with a minimum radius, keeping the assigned box. Spectators do not recognise positive or negative (inverted) spin. But for the pilot, recognizing the direction of turns and recovery action is quite a bit easier.
Indications here apply for symmetrical, fully aerobatic airplanes.
So two things you need for a spin entry, as you mentioned, are a stalled wing and large enough yaw rate. If you stall the wing inverted (meaning pushing the control column forward, instead of pulling in a classic upright stall) it really doesn’t matter at what attitude you achieved this two requirements. But the method used in trainings is as @Wirewrap explained in his answer, because it is less oscillatory and a fully developed spin can be achieved in a couple of turns.
A word of caution though; inverted spins can be very disorienting and are prone to wrong recovery inputs by the pilot. So they should not be attempted without proper training by an instructor (like anything in aviation). Good news is it’s really difficult to find yourself in one, accidentally. There is almost no situation in normal flight requiring you to apply negative g and rudder at the same time (except maybe while recovering from upright spin). I think that’s why it's not demonstrated even at CFI trainings.
After I bought a Pitts S1 but before I flew it I got instruction in an S2A using the front seat for about the same sight picture. As well as circuits my instructor insisted on some upper airwork. He demonstrated how mishandling the aeroplane after long vertical climbs, with high power and low airspeed, that the little bugger could bite. A poorly executed stall turn, (US hammerhead) resulted in a rapid entry into an inverted spin as did a positive humpty with hands and feet off the controls. Propeller effects provided the yaw on that one. I did not see much warning on either of these.
In my own machine after a year or so I built up the courage to do some inverted spins myself. The right rudder ones worked well, but the first left rudder attempt did not spin and I ended up in an inverted spiral dive!
To get my S1 to do a left rudder inverted spin (the fast one) I have to apply right aileron after the rudder to get it started.
So I recommend some caution and plenty of altitude, and know what to do if you find yourself starting to wind up in a spiral with increasing airspeed while upside down. Hint: Don’t pull back!
Right rudder upright and left rudder inverted spins are steeper and faster than the other way with right-turning engines and can be made to go faster still by moving the stick off the stop. eg the inverted spin is started with full forward stick and full (left) rudder and accelerated by moving the stick rearwards after the spin gets going. Aileron is not needed after the spin has started properly.
Flat spins must be done with left rudder upright and right rudder inverted with right turning (Lycoming) engines.
Video of an accelerated right and left rudder inverted spins in link below. Not me.
[https://m.youtube.com/watch?v=FpKaFlR98zE]
