Programming Wavelets for Audio Identification
Convolution can be used to find the note. Its best shown visually .


  Would this be a data structure holding e.g {sampleNumber, frequency} pairs?


Yes, the signal would be. The wavelet can be stored as a function but it can also be {sampleNumber, frequency} pairs.


  If a wavelet is an array of these pairs, how is it applied to the audio data?


Convolution:

$f*g = \int f(x)g(t-x)dx$

Convolution is commutative so it does not matter whether f or g is wavelet or signal or vice versa.


  How does this wavelet apply to the analysis when using an FFT?


In some applications in signal processing, convolution is calculated using the convolution theorem. 

$\mathcal{F}(f*g) = \mathcal{F}(f) \mathcal{F}(g)$

so the convolution of f and g can alternatively be calculated by

$f*g = \mathcal F ^{-1}[ \mathcal{F}(f) \mathcal{F}(g)]$


  What is actually being compared to identify the signal?


The signal is being compared to the wavelet 


  How exactly is a wavelet used digitally?


There are many applications, besides note identification, they can be used in lossy signal compression. See the Dirac codec. 

Cross Correlation is a similar operation which can be used for identifying wavelets