How to make LC tank circuits oscillate continuously?
Could anyone describe a circuit that provides a non-decaying
  oscillation?


Honestly, this should be asked at the EE stack exchange site since, for one thing, there is a built-in schematic editor.

Essentially, one can drive the LC tank circuit at or near resonance frequency with a feedback amplifier.

A simplified example of a Hartley oscillator is



The tap on the inductor allows the the battery to periodically, through the FET, add energy to the tank circuit.

Note that this is not a practical circuit as drawn but it should serve to get the essential idea across.

As the tank oscillates, the FET is driven on and then off.  You can find here an interactive simulation of a simple Hartley oscillator.