What is the primary means of IFR navigation for private pilots?
There are numerous options, and it depends highly on your route. But there are generally enough VORs scattered across the country such that you should be in range of a couple of them pretty much everywhere. As mentioned in another answer, there are NDBs, but in the continental US, generally, the ones not on an approach are getting fewer, as the FAA has followed a path of not repair them once they break. Other parts of the world, still use them and there are also NDB based airways(AIM has examples for how they can be charted on US charts).

If you had to plan a  flight from a field that doesn't have a navigational fix, and you don't have GPS, you'd start by looking for airways near where you are. Once you find some that go in the general direction you want to go, you start figuring out intersections near that or how you plan to intercept the airway. Then you end up most likely planning a zig-zag course following airways towards your destination.