This is going to vary by historical subject, but generally speaking, you don't use material locked away in private collections. You usually use material from said private collections that has been obtained and processed (catalogued) by an archive. It is the archivists' job to seek out and get access to collections. Historians can help this, inasmuch as they do occasionally get asked by people about their holdings and what to do with them (for example, I recently corresponded with the daughter of one my historical subjects who passed away, and helped her find archives that would take his personal papers).

In terms of finding them in the first place, though, we don't go looking for archives first. We go into our study with a historical question, and we follow that where it leads. This often results in us looking into the work of specific people or companies or institutions, and then poking around for records. Sometimes you end up speaking to the person in question (if they are alive), or a relative, or finding out that company X was bought by company Y several decades ago, and so you can contact company Y and see if they preserved those records (though corporations are usually pretty bad about this kind of thing). So you do occasionally find some new source this way, and it is part of the responsibility of a historian to try and put archivists in touch with that source so that these records are accessible to other historians in the future.

If you do oral histories (interviews with living historical subjects), you also always ask about their personal papers and their possible future archival deposition.

But generally, again, this is a pretty minor part of job. Most of the materials we work with are already in archives. And yes, that definitely means that we're only looking at a subset of all possible materials... such is the nature of this endeavor though. You're never going to see everything.