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For example take this paper[PDF]. If I wanted to add Weather degradation into a clear photograph would it be worth it to look at that paper and try to reverse it? Also is there any specific approach to reversing an algorithm if it is at all possible?
Draemon is correct, there is no general approach. In your case, I would read the paper.
Whether you want to add or remove weather degradation, you need to know what weather degradation looks like. That paper will have information on that, and might have an easy answer.
An example might be a paper on breaking a substitution cipher. You can certainly read the paper to learn how to encrypt something with a substitution cipher.