You know the trick of stealing a square of chocolate, invisibly, from a bar? Which is a tasty way of explaining how I recently cut nearly 10% of a novel, without changing a single thing about story - plot, character-in-action, dialogue, description - which actually mattered. The effect was like taking off a veil and earmuffs and plunging back into the story: everything was exactly the same, just infinitely more vivid. So, what got cut? Or, rather, what particular things got interrogated fiercely about how necessary they were, or weren't?
More speech tags than you need, where you could just used physical action and proper layout to keep the reader straight. Which isn't to say that a well-placed he said in the middle of a line of dialogue, though not necessary in strict fact, doesn't sometimes shape the rhythm better. It may also provide just the right pause-of-thinking for the significance - the drama of character-in-action - to flower in the reader's consciousness. Your decision.
More varieties of thought tag than you need. These are all part of what Janet Burroway, following John Gardner, calls "filtering", and though I don't think that's the best name for it, it is an absolutely crucial concept, so do follow that link to the best explanation I know, by Leslie Leigh, and then come back here. And once you understand what filtering is, what might you do about it? We, the computer generation should be thankful: I did, one by one, a search for seemed, wondered, realised, remembered and thought - you'll have your own particular equivalents - and considered each one carefully. Yes, about 70% of them went, like filleting out the veins of fat in a piece of meat. But 30% of them stayed. Why?
- Particularly when I was further out in psychic distance, and the narrator was in charge, it was very natural to say things like: She put her hat on, tied her scarf tightly, remembered him in the pub, and realised he was an idiot. And so I left those there.
- And sometimes what really mattered was that moment of her realisation, that turning point for her: As she climbed the hill and looked out over the sea, suddenly, clearly, she realised he was an idiot. (Mind you, I might then have to perform a partial suddenly-ectomy). It doesn't work in the same way at all to say, She climbed the hill and looked out over the sea. He was an idiot.
- And finally, sometimes in Free Indirect Style you do need a she thought, as in the Emily/coffee example in that post, just to keep the reader straight.
Explaining the mechanical links. Get in late and get out early, say the thriller writers. Bus journeys, bullock-cart-harnessing, arrivals, routes ... You'd be surprised how un-bothered readers are by how your MC got home from the far side of Hong Kong (or Mars) at three in the morning: or, indeed, by how she got there in the first place. (Although you probably need to know, because we'll intuit if it's simply impossible, even if we don't stop to work it out.) More broadly, fiction is narrative, not just a series of juxtaposed scenes. You don't always want to end on the Eastenders' ringing doof-doof-doof (the writer's equivalent being *-*-*) after the last dramatic line of the scene. We don't need to get characters on and off an open stage, as Shakespeare does, but the stage blackout, the film-maker's jump-cut, can become a cheap high. Besides, sometimes part of making the story and setting and characters-in-action fully alive is to get us moving through their world. Don't assume, in other words, that helicoptering us straight into the crisis moment and out again is the best way to keep us involved.
Explaining what's about to happen. I love a bit of foreshadowing, as my post on the opening of Dick Francis's Straight shows: as a reader I want to sense the storyteller's hand. It's all about explicitly making the promise, as Pixar's Andrew Stanton puts it, that this story will be worth my time. But it needs rationing, and handling: is your Tell that the picnic was (will be, for the reader) a disaster, before you Show us, actually a fantastic promise of excitements to come, as Dick Francis's is? Or is it a bit of scaffolding you should take down: throat-clearing or note-making of your own to get yourself into the scene? Or is it simply a plot-spoiler?
Explaining what is happening. As real-life characters-in-action we think - make sense, remember, understand, analyse, worry, look ahead - while also acting, but that doesn't mean that it should necessarily go in the narrative. If your narrator or your viewpoint character mentally comments/explains/worries about everything as we go along, it can enfeeble the forward drive of character-in-action. On the other hand, understanding is part of what makes us then act, and fiction is not drama: it's the pre-eminent way for humans to get under the skin and inside the head of other people. So don't, please, shy away from entering your character's consciousness and conveying their thinking to the reader, nor from letting your storyteller explain things sometimes. Just think hard about when you should, and how to do it. We're talking psychic distance again, in other words.
Explaining what has happened. Just as my poetry student realised what so many poets know - that all her draft poems were improved by having the last two lines cut - so with stories. You can have a highly dramatic scene, but how much of the mental and emotional fall-out, run-out, follow through, should we have? How much does the MC need to work out - or do we need to see being worked out? Thinking really does matter, especially the sudden, epiphanic, reversally-type understanding that will drive the next part of the plot. But, as with thinking/understanding mid-scene, if every time something happens it's thought through and explained, and that understanding is handed to the reader on a plate, it has an enfeebling effect on the narrative drive. If plotting is all about playing Fortunately-Unfortunately, then don't, every time, make it a game of Fortunately-Unfortunately-ButSorted.
And you know what I realised as I was working? All these points can be grouped together as "too much explaining": explaining slightly more than the typical reader needs. So, when you do your Search, and say, "Does the story need this?" what you're really saying is "Does the reader need this?" In need I would include not simply mere plot-mechanics, but also emotional, affective needs to live in the story, and the need for the sound and rhythms of the words to work on us as much as the sense. In my case, I found I do about 10% more explaining than I - as my own representative reader - actually need. Pass me the paring knife...