What are the rough steps in obtaining and processing an image from an infrared camera?
It's hard to give a lot of useful information without knowing the details of the signals you are getting from your hardware. Typically the output from any camera is an image, so you would need to decide what is wrong with the image before trying to come up with image processing techniques to solve that problem, you don't seem to have a clear problem specification at the moment.


  What is the difference between preprocessing and processing?


Semantics. It doesn't refer to anything specific in the signal processing domain.


  Is there a preferred order to performing this steps?


Yes but you need to decide which are necessary before worrying about the order.


  Are some absolutely necessary, while others not so much and can be skipped?


It depends entirely on your source data. If your IR camera outputs a clear crisp image that contains all of the information you need then none of the steps will be necessary. If the image is completely washed out then you will need to do contrast enhancement, otherwise it can be skipped. Really nothing useful can be said without more information about your data.


  How would this differ between processing normal light vs IR radiation?


The usual caveat applies that it depends on your data but in principle there is no difference, you are just capturing a different part of the light spectrum.


  Is that roughly the correct chronologically description of the whole process?


No not really, the process will be informed by your source data and your desired output. It's unlikely that all of those topics will apply, more likely one or two of them will and not necessarily in any particular order.

If you want more concrete advice I suggest you explain your procedure in more depth, with the specifics of the data you are acquiring and the results you expect.