Ooh, this is a fun one. In general, I don't have a set template to how I write my stories, but I do have some common practices, yes.
Inspiration usually just come, I can identify the specific source for only about a quarter of my ideas, the rest just apparently randomly pop up. After the idea I usually have a cooking period, when I let it ripen in my head, only make notes of specific details and phrases I may or may not end up using. I often also chat about the story with my friend (who's a bit of an odd bird in that she lives in a social media void and her sole fandom contribution is to help me sort out my stories and beta them, so from my point of view priceless) at this point. The length of the cooking period varies a lot (from mere hours to literal years).
When it comes to writing, I may have one or more projects that I'm actively working on at one time, but I do try to (especially these days) focus on finishing them. And here's an non-sponsored product placement, I use Scrivener, which is such a good tool for building stories and keeping a track of them, something like
These Are My Hands would have been so much trickier to accomplish had I been using a regular word processor.
I've also worked on trying to eliminate the necessity of inspiration, to be able to put down words regardless of my moods, and I've done pretty well with it. Basically (around 2015 and 2016) I just made myself write every day (to a reasonable degree) with a target amount of words, and sometimes I reached it, sometimes I flew past it, sometimes I could barely manage a quarter, but after a while it did become easier. These days writing is a pretty comfortable habit, and while I might feel eh about it, I'll still sit down and when I've actually started writing it tends to work. Not every day, there definitely are times when nothing happens (looking at you, yesterday. Today's word count is 890), but much less frequently now.
When the draft is done, if it's a long one, I'll usually take a break for at least a week and then read it to see if the plot hangs together and if I need to add or remove or change something. My friend does the same, and after these adjustments have been made comes the fixing of grammar and spelling, working away awkwardness of phrases, and beta reading. With short stories the plot is simpler and doesn't need the extra work, so there's just the general editing.
Then comes the time to let the story out in the world. I think I've found a pretty good equilibrium here too, I write for myself first and like what I do. The level of execution varies as it does with anything, but you just have to let go of things even though they're not perfect, maybe the next one will be better. If other people like what I wrote it's great, I treasure every kudos and comment, and I honestly like talking about my stories and will probably have a lot of words in response to any question I get. But the reception of the stories is not something I hang my self-worth on. If it was I'd probably put more energy to promoting my work, try and figure out optimal posting times etc.:D
And of course, when one story is posted, there are a lot more waiting in the wings for me to start working on them. My current WIP and idea list has 23 stories on it, and it seems to steadily grow (last year in February the number was apparently 17...)