I used this approach to develop a natural spring for my use.
The key points are to isolate the spring water and its source from any potentially icky water coming from the surface.
Think worst case scenario: something pooping right above your spring followed by a heavy rain to wash it over your spring collection apparatus.
Also make sure you don't dig down to below the ground level of your spring in close proximity (5-10'?) or you risk opening up an easier route for the water to escape, bypassing your spring altogether.
Here my actual set up:
What I started with:
Under construction:
Complete:
Video: