The Colpitts oscillator is a time-tested design — from 1918. [The Offset Volt] has a few videos covering the design of these circuits including an op-amp and a transistor version.

The circuit is very simple — a one-transistor Colpitts oscillator with no power amplifier, and thus very limited range.

10 to 1GHz oscillator circuit schematic Wide range oscillator parts list If the frequency range is narrow, a parallel-resonant circuit should be connected between the output pin and +Vcc, to form the ...