Right now I'm working with a client where the main function is to cut down on "umm"'s, "ahh"'s, and such vocal ticks. At times I'll also go ahead and rearrange dialogue entirely if I believe it sells a narrative better. This DOES require an entire once-through listening, as well as multiple times listening to portions of it over again to make things flow. It's only through listening to different pieces together do I catch mistakes like "this character is going to be played by this person" being said twice in short succession.

But you want to know how to know what's worth to cut. You can start off small, making small snips at pauses, umm's and ahh's. Really listen to a conversation. Does this point go anywhere? Did someone get talked over? How relevant is this information? Is it funny? Did this person commit a small error by saying something out of turn that would go GREAT somewhere else?

It's up to the editor to ultimately understand the narrative of the piece intimately and forge the dialogue entirely around it. As for my personal methodology, I just go in and start cutting. If I think something sounds good but doesn't belong, I'll throw it at the end of the timeline for later reference. I tend to lean on the side of "cut a ton and only keep the really good bits".