If it's an unmolested 60s machine it will have been fitted with contact breaker points under the flywheel so assuming that it's not been updated to an electronic system, you have a choice, remove the flywheel and clean the points or find a used working electronic coil (Magnetron) and fit it in place of the existing one. A Magnetron coil is identifiable by a "lump" between one armature leg and the coil. Fitting a Magnetron coil avoids having to remove the flywheel either then or ever again! *
If you are going for the points and assuming that your machine has a top mounted starter (pull the rope out sideways) it has a stater clutch which must be removed before you can tackle the flywheel. There is a tool to grip the lugs of the clutch which unscrews anti clockwise but with care a block of wood and a hammer or even stillsons will do the job. Under the clutch is a Belleville washer - note which way up it goes. The flywheel is probably drilled for a puller but with care can be removed without the "proper" tool. However do not use a legged puller around the rim and at all costs don't hit the starter clutch spigot with a steel hammer - preferably don't hit it at all! Get the fingers of one hand under the flywheel, take the weight of the machine and tap the keyway side of the flywheel sharply with a copper hammer. With a bit of luck the flywheel will release. If you have a side mounted (pull up) starter there will be no clutch but a nut.
From there on in, clean the points, remove the plunger and clean it and make sure that it is free moving, refit the points and set to 20thou.Refit the flywheel (note that it should have an aluminium key not steel) and tighten the clutch to 55ft lbs or **tight.
* The book will say that when carrying out a conversion the flywheel should be removed and the points actuating plunger replaced with a blanking plug , but.............!