If it suddenly stopped then I'd check the points - they can close unexpectedly and the car will then not start. If the points look fine, check for a spark at the plugs - you can use a bit of wood to reach the starter if its the pull-lever type. Remember to reset timing whenever fiddling with points. If no spark at plugs, work back through leads, cap/rotor, condenser, coil, wiring as that is both their order in the system and in the unreliability stakes.
Fuel system likewise - first check there is actually some fuel in the tank (clear fuel lines are handy for this, otherwise the pump test below or dip the tank - you should also be able to smell the engine flooding if you've been trying to start alot), pump, then carb.The pump is easily checked - disconnect the fuel pipe from the carb and direct it into a cup - then get someone to turn the engine over - no fuel and its a blockage or dud pump. A pump takes minutes to replace. If fuel flows and the ignition is okay, then its likely the carb which is a pain. If you don't have one, fit a fuel filter.