How does this oscillator work?
The FET is used as a common source amplifier.  It will amplify voltage from its gate to its drain.  It can amplify well over unity, but the polarity is negative, which would normally prevent it from oscillating.

The trick in this case is the capacitors and the inductor phase shift the signal enough at the right frequency so that you end up with positive gain from gate to drain.  Adjusting the inductance tunes this frequency.