How to implement an Equalizer
FFT wouldn't be my first choice for audio equalisation. I would default to building an EQ with IIR or FIR filters. FFT might be useful for special circumstances.
A commonly recommended reference is the Cookbook Formulae for Audio EQ Biquad Filter Coefficients.
A java tutorial for programming biquad filters. http://arachnoid.com/BiQuadDesigner/index.html
Is there a good book about DSP programming that explains equalizers ?
Understanding Digital Signal Processing is a good introduction to DSP. There are chapters on FIR and IIR filters.
Intoduction To Digital Filters with Audio Applications by Julius O. Smith III.
Graphic Equalizer Design Using Higher-Order Recursive Filters by Martin Holters and Udo Zolzer is a short paper detailing one EQ filter design approach.
There are many different ways to obtain an equalizer, and as Shannon explains, the IIR/FIR filter way is one of them. However, if your goal is to quickly get an equalizer up and running, going the FFT way might be easier for you, as there exist a wealth of reference implementations.
As to your question of FFT size, it depends on what frequency resolution you want your equalizer to have. If you choose a size of 16, you will get 9 (8 complex + 1 real) channels in the frequency domain equally spaced from 0 to fs/2. The 1st is centered around 0Hz, and the 9th around fs/2 Hz. And note, some implementations return 16 channels where the high part is a mirrored and complex conjugated version of the low part.
As to the implementation of the equalizer functionality, multiply each channel with the wanted gain. And if the spectrum have the mirrored part, mirror the gains as well. If this is not done, the result of the following IFFT will not be a real valued signal. After multiplication, apply the IFFT.
As to the difference between a FFT and filter based equalizer, remember that a FFT is simply a fast way of calculating a set of FIR filters with sines as impulse, critically sampled (downsampled with the filter length) and evenly spaced center frequencies.
Regards