The thing I have found helps A TON is writing drabbles. They are very short stories, that has to be exactly 100 words, no more, no less.
I always start out with a word from a random word generator, or a theme, and then I write a little story, not worrying too much about the word count.
And then comes the editing part, where I have to cut everything away, strip it until it is just the very bare minimum, and exactly 100 words.
Meaning that I must kill a lot of darlings I have just met/made.
And yep, it's super hard. And it sometimes hurts. But it also really helps me realize just how much I can cut out, that either makes the message of the story weaker, or doesn't help it at all.
So I would recommend that as a first step, so you get the practice and experience with editing things that might not be AS emotionally attached to you.
Another thing is to question your writing as a reader.
A story that's really well edited doesn't have anything that isn't necessary for the plot. Ask the questions about if it helps move the plot along in any way, or if you are trying to work around it to MAKE it work with the plot. If it's the latter, cut it.
That said, it's really really hard, of course, especially when having put super much time and effort into it...
But like a band-aid, it's better to just give it a clean cut and then tie up loose ends afterwards.
Depending on the story, however, I also think it's not always necessary to cut into the bone. I have a story that I enjoy writing as well as reading, which isn't edited into the bone, as that would make it into something else entirely.
So it mostly depends on what story you want to tell, and what message you want conveyed, I think.