but everything has a fundamental or a dominant freq, so you can basically search for a specific freq something likes to resonate at.
No that is not correct, especially with impulse sounds like a clap. If you take the FFT you will see the distribution of frequencies changes rapidly with time, so their is no one signature spectrum for the sound.
An envelop detector is an example of parameter extraction, which is more likely to succeed than a full frequency analysis. Another popular parameter is zero crossing timing.
Once you have these parameters extracted at many points at during the sound, you can then compare them to a template or standard sound. As you are comparing many values with many values the answer is not a simple yes or no, it is more like a probability. You then set a threshold on a probability that you want to use in order to differentiate a clap from some other percussive sound you might pick up. One way of comparing templates is to use an cross-correlation:-