How does an oscillator oscillate?

Oscillators generally consist of a capacitor and inductor wired in parallel. Current is passed back and forth between the two.
The capacitor is charged via an amplifier which then discharges into the coil. When the current stops flowing, the field collapses in the coil, recharging the capacitor.
It will do this at a frequency, determined by the sizes of the coil and capacitor. This ringing or 'oscillation' would normally decay to nothing.
In an oscillator circuit, an amplifier is connected with the output of the tuned circuit connected to the input. This will keep giving the tuned circuit a kick, continuing the oscillation for as long as power is applied.