This is just going to be a short instructable because of its simplicity. This only works with the speakers that have the positive and negative wires that hook into a stereo. To tell if the speaker is blown or not without taking it apart is really easy. All you have to do is take a 9 volt battery and touch it to the wires. If it makes scratching noises its good. If it makes no sound at all its blown.
A lot of times speakers don't have sophisticated crossovers in them, just non-polar electrolytic capacitors, and the caps fail more often than speaker drivers. Although I've burnt out a lot of tweeters over the years myself. Most tweeters can't handle too many watts.
Usually this test is done with a 1.5V cell (AA), just to test polarity (positive battery to positive/red speaker = cone pushes OUT).