Designing an Oscillator
Of significant importance is the capacitor on the input to the inverter. The phase shift between output and input has to be 180 degrees for oscillation, and the XTAL and capacitor together produce this phase shift. If you look at the equivalent circuit of the XTAL and fed a signal in at the right frequency then looked at the output across said capacitor you'll see that phase shift. That's why you can push up or down the frequency a little bit when you vary the cap: -



In the above example I've set the equivalent circuit of the XTAL to be: -


L = 8.45mH
Cs = 0.03pF
Cp = 6pF


As you can see in the lower graph the phase shift between the limits of the series and  parallel resonance points falls to 180 degrees.

There is a lot more subtlety to it than what I've shown but hopefully this is enough to help.