How do you find underground pipe and wires to a private well and how deep would they be?
If your water does not freeze up in the winter, they are presumably buried below frost line for your area - which is typically where they do get put by competent installers (and not terribly deep if there is no frost.)  In my area that's 4-5 feet, typically. In most but not all cases it will probably be the shortest, most direct path from where it comes out of the house to the well. The only way to be sure is to carefully dig down and find it on either end, and then use those locations to try and find it nearer to where you might be damaging it if you blindly pounded things into the hillside.

Once you have found a few specific points, be sure to witness them in one or more of these methods: 


take very careful tape measure distance readings to fixed objects
(the well-head if it sticks out of the ground, the corners of the
house foundation, other objects likely to stay put for a long time)
and write those measurements down on a map - you can then construct a
triangle to find the pipe again by measuring from a fixed point as
recorded on the map and making an arc, then doing the same from
anther fixed point - where the two arcs cross, the point you
measured the well-pipe at should be below (within some scope of
error.)
I'm fond of a more direct approach, where I construct an annual
flowerbed or easily movable perennial plants flowerbed as a physical
witness to the item below. You'd still want to save a map with the "important house paperwork" and hope it doesn't go missing, but there's no doubt where to dig unless someone obliterates the flowerbed in question. If you remember not to move it, some sort of lawn decoration could serve the same purpose, but a flowerbed is more lasting. 
A section of inexpensive PVC electrical conduit just shorter than the depth to the buried item and marked (both what, and from 0 at the bottom to how long it is at the top as a measuring device) with permanent marker can also be buried in the hole as a guide to future digging. The idea being that you can find it quickly as it's just barely buried, and then follow it down and know how close you are to the buried item.