I could believe this is the hardest part of mastering the writing craft. It has happened to me few times already. I've been able to delete entire paragraph(s) from a short story. But it doesn't happen as often as I would like it to happen, I am horny for more slicing. I believe I've become quite okay at removing redundant unnecessary pieces of texts as "lazy writing", but most of the time, I end up with longer text after every rewrite.
Sure, the details might occur only later with maturity and rewriting might be an additive process most of the time. But I like certain things the way I like the boobs, subtle enough to fit the context, and, in absence of better words, quite often less is more. But my stories just get bigger.
But, my hopes are, that I am not alone with this problem, and maybe someone has some good ideas to be shares about the topic (which is not the boobs). I've pretty much gone trough all the writing craft essays here, but I might need some digestion before all of it starts to fit the picture, though I believe that hardly any of them had to do with removing text, just methods to avoid "lazy writing".
Craig Clevenger uses a term called "Shark Music" that I've always found to be a great descriptor. It's in a craft essay on this site, something that should usually be killed. Similarly, any of the sort of "editorializing" done by the narrator I have to reconsider, sometimes it can be a focus of a story and sometimes it can just get in the way. There's also a good essay on this site recently about redundancy.
Any of those sort of tangents of backstory that relate thematically to the present action, it's something that most novels do very well but I feel like I have a hard time with, those are usually the bigger sections I ponder over cutting or keeping. How often do they absolutely need to be part of the overall story?
Exposition I think is best when it's like 3 sentences or less. If I can't edit exposition to a couple sentences I'm happy with then I at least have to break it up to feed more info at parts were it's absolutely absolutely necessary.
I do a revision, just for removing words. No additions, unless they replace the words I just removed. I also found that you can remove a fair amount by searching out the words 'just', and 'that.'
Also, take out all the adverbs. It's really important.
If that doesn't work, you could also then try taking out all the other words.
I find taking out words weirdly pleasurable.
For practice, take one of your stories, and see how many words you can cut, how many sentence you can tighten, before you are no longer able to tell the whole story. You don't have to like uber-economic writing as a style, but it's usually a valuable exercise. An alternative is to do it in reverse, think up a fairly complicated narrative and set a really strict word limit. I've found it's a lot easier to start out writing a "clean" draft and then flesh it out, than it is to trim a wordy first – or second or seventh – draft while revising. You can't give someone a chocolate cake and then tell them they can only have apples from now on because apples are better for them, and expect them to be happy about it.
I took out about 250 words on a 19,000 word story on a 'just and that revision' yesterday. Also removed a few uses of 'at the time.'