Just below the topsoil is solid rock. The only way to drill a well would be, well, a well drilling rig that can dig through rock down to a water source.
In some areas, there is no rock just below the topsoil. You can pound a sand point by hand down pretty far to reach a water source.
A sand point is a pointed perforated section of pipe. You put a cap on it that's made to take hammer blows, and you pound it into the ground. Remove the cap, add a section of pipe, replace the driving cap and repeat.
Here's a kit. There are many videos on youtube showing how it's done.