Recently I've been struggling something epic over a challenge story I'm trying to get finished, and I've been thinking a lot about the ways I get out of my ~funk and finish things. These are the tips I would give; they really genuinely work for me. Also I'm fascinated to hear what other people do, so please share!
+ Read other fic. It doesn't even have to be in the same fandom. I just find that it gets so many synapses firing re. your favourite things about fic, your kinks, things you like to see in dialogue, little scraps of ideas you want to use.
+ Take a shower. Seriously. Leave your writing and just go stand under the shower. It helps.
+ Ignore grammar, capitalisation, punctuation etc. I don't know if this will work for everyone, but I find that if I abandon these things when I'm particularly stuck, my writing tends to flow a little more in terms of plot and movement and character development. It just feels a little less structured and confining. I think this is because personally, when I'm stuck, I feel so boxed-in and anxious, almost like I can't breathe.
+ Post what you've written. Not publicly, but there's something about seeing even a small portion of your work posted and looking all pretty that helps you keep going with it. I also find it easier to edit this way; so much less messy.
+ Visualise what you're writing about. This sounds stupid and obvious, but a lot of the time when I'm stuck I catch myself not picturing what the characters are doing in that particular moment, but rather how the story will look from the outside; how it will read to someone, what people will think of a particular turn of phrase or action. It's so easy to get distracted from this really fundamental aspect of writing. If you're not thinking about the characters, it's not going to translate well to the reader.