I think where you're lost is that the FFT sample size determines the number (and therefore size) of the bins, while nyquist determines the maximum frequency that can be binned.
If you have a window of 8192 samples, for example, that gets you 4096 bins. If you're sampling at 44100hz, those 4096 bins gets you bin sizes of around ~5.38Hz per bin. So your lowest frequency range that you can identify would be 0-5.38hz, then 5.38hz-10.76hz, etc, up until 22044hz-22050hz. So if you're sliding a window of 8192 samples with a sample rate of 44100, that's about 18.5ms per FFT window. That means you can draw a spectrum with a resolution 4096 bins per 18.5ms of audio. If you wanted to plot a spectrum with a finer time resolution, you'll have to give up some frequency resolution by having smaller bins.
The actual results vary by FFT implementation, and it's common to have windowing inside the FFT that I don't really understand, but has something to do with the accuracy of those bins by preventing leakage of one bin into another. "Hamming Window" is probably the most common and usually happens by default, but that's a different window than the window you're sliding through the time domain to take FFTs on and plot.
As a user of FFT, at least for audio stuff (RF might be different), you mostly just think in terms of bin size.
edit: I did it wrong, fixed the numbers (I think)