I'm terrible for starting stories and not finishing them. A few years ago I realised how unfair that is to readers if you leave them part published, so now I have a rule that I won't publish a new story unless it is complete. Although this needs serious will power! Right now I have about 8 good, solid stories that are part written to one degree or another, with about 3 more in development. I've long since stopped beating myself up about not finishing them and just dip in an out of which ever one takes my mood at the time. I tend to spend a few months on one before I get bored and change to another one. So I am quite good at picking up on stories that have been shelved for months or even years.
Things that work for me when picking up and old story:
1- Read it from the beginning and edit as you go. This is the best way to get back into a story, but if there is a lot of content then it takes some time and effort to do, but it's worth it (I've just picked up one that is about 95k words and did a complete re-read and edit before writing again). Once you've done the read through/edit your mind will be back in the story and you'll be able to pick up where you left off.
2-Short read through. If you are familiar with and remember all the content well, then just do a short read through/edit of the last few chapters or whatever and pick up from there.
3-Make continuity and future plot ideas notes. I write on word docs using chapter headings to easily jump around the doc. At the bottom of the doc, around half a page below what I am currently writing, I have 2 sections. The first one I head 'Remember' and is in bullet points. Here I put stuff I need to remember to do for continuity and other small things things. For example, a character is big on yoga, I'll drop a reminder in the remember section, so that I know to put the occasional reference to yoga every now and then. Or if a character makes a commitment for the future that you'll need to remember, like 'lets visit Susan next month', I'll drop it in here so I remember to write it. The second section I keep at the bottom of the page is plot ideas. Time and life often get in my way when I am writing, and if I am in a good flow it's really annoying to have to stop. So I'll write a few notes, sometimes as much as a few paragraphs, about what is in my mind at that time for the immediate plot. Then when I go back to it, I can see where my mind was at and where I was heading with the next few pages or chapters. I don't always follow this, I can ignore it and go in different directions, but it's a big help to get my mind back to where I was when I left off on the previous session.
4- Don't flog a dead horse. Sometimes a story is just not worth the effort, especially if, like me, you've got lots of other options that are half written to chose from. It's a tough thing to do, but occasionally I do move it a folder marked 'old' and leave it there so I can concentrate on the better stories. Why not just delete it? Because there is still good stuff in there, maybe a character or particular scene. Every now and then I'll go through my old folder and use it for spare parts, a bit like a scrap heap, where I can find useful little bits I can place in other current works. So nothing I write is ever truly abandoned, it's either waiting to be piked up again or in the scrap pile ready to used for spare parts.