The first and perhaps most obvious trick you can try to diagnose your speakers is to listen carefully to them. Locate all of the primary speakers in your car’s sound system, play some consistently-toned music, and listen carefully to what comes out. When a speaker is working properly, you should hear the music coming out clearly at any volume.
When the speaker is partially blown, you may still be able to hear the music on a lower volume, but as you increase the volume, it’ll gradually become muffled and distorted. If the speaker is completely blown out, then you’ll either hear absolutely nothing, or just some soft noises like buzzing, ringing, or hissing.
If you’re not sure about the quality of the sound you’re hearing, try holding a microphone with an equalizer up to the speaker with the levels zeroed and the balance in the middle. If it picks up any obvious distortions, you should see them reflected in the equalizer levels.