An oscillator based on an inverter is the easiest one to use for most crystals. Putting a resistance of a few kΩ in parallel with the inverter, and having the series resistance very low or shorted will encourage overtone oscillation.
You need very specialist equipment to work out whether a crystal is supposed to be a fundamental or an overtone, but the frequency it runs at will usually give you an indication, as the crystal will be adjusted to expected mode. The 3rd overtone isn't exactly 3 times the fundamental, but it will be a few hundred ppm (parts per million) different. So a crystal that runs at 10.0024 MHz or 30.00006 MHz will most likely be designed to run at 30 MHz