How do I write unimportant details?

I think if you stopped thinking of the details as unimportant, you might find it easier.

They're very important.

You need to make your characters real - human - credible. And that's done by showing how they react to things, what else they do in their day to day lives, what they like and dislike, and so on.

Of course the plot is important, but if your readers have no feelings about the characters and don't care whether they succeed or fail, live or die, love or hate, they won't want to read your story.

I'm sorry but it's pretty simple. You write who and what you are, which is why it is art. Sounds to me like you need to get outside more and smell some roses.

Sounds like you need to combine it. A scene can have multiple purposes. Some say each scene should at least two, and I don't think that's a bad idea at all.

By all means, don't add fillers to your story, that's generally a bad idea - if there's no point for X to go to Y and see Z be tortured, then don't write it.

Realize, though, that character building is often one of the most important things in fiction. For many readers, me included, it's the most important thing. I'm not going to read a story if I don't care about the character one way or another. If I'm indifferent to whether a character lives or dies, then what's the point... you know? Ho-hum...boring.

Now I don't know what type of story you're writing, but for most plots, it helps throwing obstacles in your character's path.

LOTR SPOILER AHEAD:

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E.g. in LOTR, if the Fellowship had not been met by terrible weather while trying to cross the pass at the Caradhras, then they would never have been forced to take the route under the mountains, never met the Balrog, never lost Gandalf...

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Or take a simple scene where a 14 year old girl saves her annoying little brother by crawling into a storm drain and pulling him out.

Wouldn't that scene be much stronger if you'd had an earlier elevator scene where you show she suffers from claustrophobia? First she's outside the elevator considering taking the stairs, but it's seven storeys up, so when the elevator reaches her floor and is empty, she decides to take it, but as she goes up, more and more people enter... you can show her fighting for control, trying to focus on those numbers, feeling the panic set in etc. And at the same time of course, give her a reason to have to the 7th floor.

And how do we know the little brother is annoying? You have some scenes showing him as a real brat - and of course your characters reaction to that.