Welcome ring lord, the easy way to do this(or at least easy for me) is to:
*first remove the wrist pin from the piston (this is the little shaft inside the piston) it is held by a small "C" clip, carefully remove 1 of the clips so you my slide the wrist pin out, do not use anything that could scratch your piston to assist this out try a plastic pen.
*Now your piston is out, so remove any old debris form it.
*Apply a small amount of 2-stroke oil on the piston where the rings go, now put the rings in place (some piston rings with come with an additional little thing that resembles a piston ring but is bent multiple times to create a spring to go under one of the rings, this I have always thrown away), once they are seated rub that oil over the rings so the are coated.
*Remove the existing "C" clip from the piston and put in a new one in it's place if your ring kit came with some.
*make sure the jug is clean inside, now apply some more oil on the cylinder wall with a clean finger or two.
*Make sure the piston is facing the correct way which usually has an arrow pointing toward the exhaust port or an "EX". If it does not have these symbols, the pins that keep the rings from rotating should go on the opposite side of the exhaust port.
*Compress the rings with your fingers and insert the piston into the jug (have the jug on a work bench upside down), this should slide right in. If there is any snag make sure the rings are tight to the piston I use both hands and as many fingers as I can to keep this as I slide it in
*Now just make sure your gaskets are good to go and reassemble.
Note: Since you broke the old ring removing the piston, you may have to use a flex hone to repair the scratched are where the ring had an issue. which is probably right next to an exhaust or intake port. If this is not addressed your new rings may not last very long. A local shop will probably charge 5-10 bucks for this unless they are too good for scooter work.
P.s. What is with name ringlord? Was this sarcasm after the piston ring issue? Sorry, I couldn't hold back.
I should also mention, I am no type of scooter guru or master mechanic but this has worked for me with zero issues, I have broke not just rings but even a jug on a Aero 50 not all that long ago, when I did not want to remove the piston first for a simple ring change. I slid the jug on the new rings and must have cracked one, because I when I kick started the motor... The ring caught on the intake port which broke the port, destroyed the new rings and the old piston. Take it easy.
