How does a student pilot learn the process of pre-flighting a Robinson R22?
I have never flown the R-22 but I am rated in RH and ASEL. I can answer specifically about the Schweizer (Sikorski) 300C/ CB/ CBi helicopter.

1) How does one learn the preflight? From your instructor. During each lesson the first part of touching the aircraft should be the preflight. Legally speaking, that is after touching the log books/ registration/ weight and balance/ etc. to make sure that it is potentially airworthy in the first place. First you watch them do the inspection, then you do it under supervision, then they watch you from a distance, then the instructor finishes up whatever they are working on last while you preflight it solo (with the best instructors doing the preflight themselves before you even start).

2) How long does it take? For the Schweizer it took me probably the first 10-12 lessons since I was initially not able to fly frequently enough to remember most of what I learned the last lesson and I was working 80+ hours per week at the time. Going 1-2 months between lessons is very bad for retaining new information. Had I worked less and flown more it probably would have taken half of that for me to get comfortable doing the preflight myself.

The items on the checklist are really not that hard when you understand the function of the parts you are checking. When you check control rod integrity you know what they do. You follow them from the cyclic and collective through the cabin, up the mast, through the mixer arms, and to the swash plate. You check the swash plate. You follow up the mast to the control rods attaching from the swash plate to the rotor blades themselves. Other than the climbing around the aircraft it probably took me longer to type that than to actually do it for a preflight.