Let's assume that the battery and starter are doing their job, and that fuel is reaching the carburetor, but the car does not start, then the trouble must be somewhere in the ignition circuit. But first, before starting your diagnosis, it is advisable to give the whole system a visual inspection which might uncover obvious things such as broken or disconnected wires etc.
The best way to start tracking down ignition troubles is to begin with the primary circuit since this is where troubles show up most frequently. First remove the distributor cap and block the points open with a piece of cardboard, then turn on the ignition and with a test bulb or voltmeter check to see if there is current at the terminal on the distributor. If you do not get a reading at this point, the current is cut off somewhere in the connections leading back to the ignition switch or it may be that the condenser has an internal short to the ground. The latter possibility can be eliminated if you can restore current at the distributor terminal by disconnecting the condenser from the distributor plate so that its outside shell is not grounded. With the possibility of a bad condenser out of the way, work toward the ignition switch and test for current at each connection until you get to one where you get a reading. Between this connection and the distributor lies the trouble.
On the other hand, if the test equipment shows a current reading at the distributor terminal, it is safe to assume that the trouble is in the unit itself, most likely burned or dirty breaker points. A final positive test for defective breaker points can be made very simply by removing the cardboard from between the points, and positioning the distributor cam by turning the engine to where the points are closed. With the points closed there should be no current at the distributor terminal. If there is current, renew the points.
In an emergency, the points can be cleaned by using the sanded side of a match box, a knife blade, or the sharp edge of a screwdriver to scrape the scale from the contact faces. After cleaning the points, and a gauge is not available to set the gap, a quick adjustment can be made by using four layers of a piece of newspaper. The thickness of the paper is equivalent to about .020", which is the approximate gap setting for most distributors. Of course, at the earliest opportunity, the points should be replaced and a precise point adjustment should be made.
If the procedure outlined under "Primary Ignition Checkout" does not uncover the trouble then it will be necessary to continue the tests into the secondary ignition circuit. Secondary Ignition Checkout