What is the most common way to change fields in academia?
If this is a move within the same broad area (or a closely related field) your best bet is to get or keep a job in your own field, and then begin finding research that transects both of your fields. For example, if you're in political science currently and want to shift to, say, geography, then begin by publishing research on geospatial politics until you have enough publications in geography journals to get a geography job. Often, schools will have interests in more than one field, and so a background in more than one can be a benefit when looking to advance.

What would be best is if you are in a school that has both fields of research - in which case collaborations would be the easiest way to go. I'm currently in the process of doing something similar, but I have the benefit of being in a very broad school that has both people in my own field, and people in the field I am shifting to (slowly, but surely!).