Moon probing is striaght forward but time consuming as the probes take a while to analyse and transmit the results.
You'll need to use the Gaze(Astro V, Survey V, 5 Mins), Discovery(Astro III, Survey III, 10 mins) or Quest (Astro III, Survey III, 40 mins) probes - and equip a Launcher.
The Gaze & Quest probes can be used in Core or Expanded Launcher, the Discovery requires an Expanded Launcher due to the probes being 10m3 in volume.
The process is simple:
1) Warp to a Moon
2) Right click on the moon and "Align to"
3) Wait approx 15 seconds to ensure you're flying straight towards it
4) Launch the probe
Once the probe is launched - you won't see any countdown timer or get any feedback until the results are in. You can however warp to a safe or repeat the process on another moon before the results are in.
You should avoid leaving the system, changing ship or logging off
