How do pilots travel from remote private airports after landing?
You do whatever you can.

Sometimes you call a taxi/Uber, sometimes you walk, sometimes you pack a small folding bicycle into your plane, and sometimes you borrow the airport car.

Many small airports in the US have a car (often a retired police car) available for itinerant pilots to borrow.  It's usually a scary rusted out pile of junk, but it works.  If you borrow it you're expected to return it promptly &amp; with a full tank of gas. 

It's wise to make arrangements for ground transportation before you arrive - there's no guarantee that any particular option (except walking) is going to be convenient and available.