This advice may seem contrary to what I just posted (“Trim fat, add muscle“). But when you’re in the moment writing (not editing!), if something random comes up, don’t immediately scream ‘THAT’S NOT RELEVANT’ and move on. This is especially important in your first draft.
If you exclude absolutely everything not related to the plot, your story’s flavor will suffer. If my character decides in the middle of a scene that he’d like to talk about his mom now (or more specifically, about these pills his mom takes), I let him. Sometimes what he says shows up later in a MUCH more dramatic way!
(At the same time, though, if you have a pet subject that shows up in your story and you go on and on about it like it’s the natural history of whales, that may be a natural outgrowth of your enthusiasm–not a natural outgrowth of the story.)
Follow the story. When you’re writing down something new, write down everything that shows up–in the editing stage, it’s much easier to trim and rearrange than it is to write something that’ll fit in the empty yawning hole you avoided writing in the first place. (Trust me, I had to do it in Out Where the Sun Always Shines. It worked, but writing it in the middle editing felt really awkward).
“Pay very close attention to the first three concepts that come out–they are usually the most fresh and unhindered.”
–Luc Mayrand, The Imagineering Way