Get yourself a multimeter if you don't already have one. You can get a decent one for about twenty bucks. You can use it to check your coil quite easily. There should be at least 10,000 ohms resistance on the secondary windings (coil tower to one of the side terminals), and less than 10 ohms on the primary windings. Any significant differences or a zero reading means a problem.
After that, you can use it to figure out your ballast if any and coil. Normally, a set of points will tolerate up to 4 amps before premature "burning" sets in. That's why 6 volt and 12 volt systems run coils with different resistance factors. Ohm's Law comes into play here.
I (amps)=V (volts)/R (ohms)
To get 4 amps across the points in a 6 volt system, you need 1.5 ohms resistance through the coil. For a 12 volt system, you need 3 ohms. With 12 volt systems, the manufacturers sometimes used a 3 ohm coil. However, old habits are hard to break (and 6 volt coils were available and cheap), so they used a 6 volt coil with a 1.5 ohm ballast resistor and called it good. Then, they got the idea to bypass the ballast resistor during starting so the system got 8 amps for a short while, which aided starting and really didn't harm the components.