We present the operation of an experimental setup designed to optically measure the quantum position fluctuations of a macroscopic mechanical resonator. The resonator is kept in a cryogenic environment and its movement is monitored with a high-finesse Fabry-Perot cavity. We have designed and realized an optimized resonator for the observation of its quantum position fluctuations. It consists in a quartz micropillar vibrating on a compression mode and clamped at its center by a thin membrane. We have demonstrated a fundamental vibration mode oscillating at 4 MHz with a mechanical quality factor close to two millions. We have implemented this resonator in a high-finesse Fabry-Perot cavity. A high-reflectivity mirror is coated only on top of the pillar in order to avoid any altering of its mechanical quality factor. We have developed a laser photoablation technique in order to realize the coupling mirror of the cavity with a very small radius of curvature as well as a high reflectivity. This allows us to build a cavity with a finesse of 50 000 and an optical beam waist, smaller than 10 μm, fitting the transverse size of the resonator. We had make a dilution refrigerator especially designed and optimized for ultrasensitive position measurement, in which we have operated the optomechanical device. The whole optical setup, made of an ultra-stable laser source and a resonator motion detection device, allows us to observe thermal position fluctuations of the resonator down to about 1 K.