On the left side handle bar controls there are two levers silver one is the rear brake and the small black one is to engage to pressure plate. Since you can get the lights to turn on you have already figured this out though...
Pull the plug connect it to the spark plug boot and touch it to the cylinder head. Depress the black lever and turn the pedals over. You should have a nice blue spark jump the gap. If you do not the kill switch is either in the off position (switch on right side of bars), or there is an issue with the wiring on the bike. Puchs will not start if the horn is not correctly hooked up, I normally remove the horn from the circuit since it sounds like a asthmatic duck when it actually works. The horn is mounted behind the headlight and should have a blue/black wire and a brown wire coming off of it. Remove the blue/black wire and ground it directly to the frame.
If this dose not work you get to delve in a bit deeper with wiring. There are 4-5 wires exiting the motor (depending on the year of the bike) right under the carb (under the left side panel). These wires bridge into a connector that is directly connected to the coil (right side panel). The blue wire coming off the motor goes into the bridge and a blue wire and a black wire should exit the other side. The blue one goes to the coil and the black one goes up to the kill switch. If the black wire is grounded you get no spark, remove it from the bridge to make sure there is not something wrong with the kill switch (stock ones go bad and will permanently ground the black wire). Check for spark.. If you still have nothing check the ground coming off the wiring (all ground on the bike should be brown). there is also a ground wire coming off the other side of the coil that should either go back to the wiring bridge or ground to the coil body.'
If none of the above works for you my money is on the points not opening (pull the round cover with the puch logo on it and shine a flashlight into the magneto. They should open between .018-.020 somewhere BTDC. If they don't open you can adjust them with a flat head screw driver.
After ya get spark you should consider cleaning the carb out and getting some fresh gas. Carb comes off by loosening the air box from the carb and the carb from the intake, wiggle the carb off the intake a bit and then turn the carb towards you 90° and pull it the rest of the way off. 14mm wrench will get you into the float bowl and a small flat head will get the jet off. They really get varnished up over time or get a lovely coating of white powder.Be super careful of the float bowl gasket since they are cheep paper gaskets and can be a bit fragile, also don't over torque the bowl during re-installation because the threads on the carb are aluminum and will strip out.
Here is a link to the puch service manual, has pretty much every bit of info you could ever want.
Manual
Good recource for info is
Moped Army
Shoot me a PM if ya can't get her started and I can offer more options.
Here is project puch. Too much time and money invested...
