I wrote a book about this. I worked as the historian on numerous excavations that my agency funded. It began as a great experience, but I found, as the years passed by, that there was a fundamental flaw in the collaboration.

Typically, a historical archaeological excavation begins with an archaeologist with a research design and a question/hypothesis that the archaeologist describes. The archaeologist then hires a historian to research the selected site and to find as much as possible about the site and people involved there.

The excavation proceeds, followed by the lab work, followed by the writing of a report. The historian may be asked to write a history chapter describing what written sources say about the site. The bulk of the report consists the archaeologist describing how the site fits in with the original research question and the research design.

I found this process to be fundamentally flawed. By the end of my tenure with the funding agency, I turned the process on its head. I pointed out to the archaeologists that historians have a broad set of topics and issues that are being debated in the current venues, and that these represent a spectrum of possible research questions that could be addressed. Archaeologists typically treat historians as though they were grad students directed to research local records on a property - something they, themselves, could do (and frequently do). The archaeologists may have intuitively understood that they needed a historian, but they rarely understood how to use one properly. I insisted that the site selection and research design begin as a co-equal collaborative process. That way, the historian would be able to inject questions current in the historiography of the topic. Selecting the question(s) to be addressed was a give-and-take process, but that is the nature of collaboration. The historian ceased to be the flunky who searched property records and instead became a scholar who brought the benefits of another discipline to the table at the beginning, middle, and end.

That's the way, I concluded, things should be done. That's not the way they are normally done.

And to answer your final question - 'Does s/he try to find an archaeologist interested in performing the relevant fieldwork?' That is rarely the process. I eventually began to work that way because I administered a funding agency that dealt with archaeology, so I eventually was the one who approached archaeologists with an idea, but that is the exception, not the rule.

In my book, I also point out that while archaeologists would benefit from true collaborations with historians, historians need to look to historical archaeology for insights. While I found that the relationship between archaeologists and historians was flawed, I also describe how the relationship between historians and archaeologists is typically non-existent. I found the approach of most historians to be also flawed because many - or perhaps most - do not consider material culture in their research. That, too, needs to be corrected, and my book describes how that can be accomplished.