I might be able to help; I spent my whole young life moving from project to project without finishing anything. Now I am a casually famous horror author whose work is unusually popular on YouTube, and my second book was optioned for a film.
1. Keep a notebook with you
I keep a large, college-ruled notebook in my backpack with me at all times. That backpack comes in the car with me, it goes to the office with me, it goes on hikes with me. Any time I get an idea for a story, I write the idea out in bullet points on a page in the notebook. Then I write a working title of the idea on the inside cover of the notebook, in the style of a table of contents.
The purpose of the book is not just to capture my ideas. It's to alleviate the burden of having an idea baking in my head all week, compelling me to abandon a current project and start a new one "while it's hot." I often forget about my ideas after I've written them in the notebook, only to return to them a month later and go "Wow, that one was good. Let's do that one next."
2. The Tattoo Rule
Some people just walk into tattoo parlors because they want a tattoo. Any tattoo. Maybe a cool skull? They do it because it sounds exciting, but they have no real investment in the piece and come to regret it years later. A rule I learned about tattoos is "Sketch out the idea, put it in a book, and stick the book on your shelf. Open the book in six months, and if you still like the art, get the tattoo."
Authors get really excited about the ideas that bubble up in their minds throughout the day. Sometimes their enthusiasm causes them to over-commit, and they start pounding away at a new story, novel, or blog post while the idea is still fresh in their mind. Don't do this. Have your excited reaction to the thought, jot down a few notes on it in your notebook, and carry on with your day. At the end of the month, review your notes, and pick the ones you still feel committed to. You'll find that most of your ideas were passing fancies that don't withstand the test of time (and that's why they never get finished even when you do start them in earnest).
3. Finish your project
Your post is asking "How do I finish projects?" so it's silly to reply "Finish your projects." But let this be your mantra: finish your project, singular. Work on only one project at a time until you can stabilize your output. Then allow yourself to do two if you feel the need. As a personal rule, I never exceed two. You only have so much energy and spare time, so if you spread your efforts over a large number of projects, it becomes unmanageable and nothing gets done.
The other side of this is, learn to identify which types of projects you never finish, and which types you do. What is it about these completed projects that maintain your engagement? Is it the fan response? Is it the subject matter? Is it the medium through which they enter the world? If you love writing but you aren't finishing your projects, maybe you're just doing the wrong projects.
4. Spend time identifying your inhibitions
Art is an act of expression. You have to learn about yourself to figure out what you want to write. If you aren't finishing anything, it might be the case that you have the innate urge to write, but on some level you don't know what to write.
I spent six years writing fantasy books and never finishing any of them. You know what I realized after all that time? I loved fantasy video games, not books. Once I had that revelation, it was easy to finish my books, because they all became horror/thrillers.
Or it might be something else. Are you sensitive to criticism of your work? I am so sensitive that on occasion I'll get a bad YouTube comment or book review and it'll mess me up for days. I can't advise you on overcoming that sensitivity because I myself have not discovered the answer. But some good advice I've gotten on the subject is...
5. Foremost, write for yourself, not for your audience
Fans are fickle and fan service is an exercise in futility. You will never make everyone happy, you will never avoid criticism. And even if you do get popular, your popularity will ebb and flow and wax and wane. All of it hurts, because your writing is an extension of you. It's easy to interpret criticism of your work as criticism of your identity.
But there's one way around: write what makes you happy, and write it because it makes you happy. There is great satisfaction in completing a project, even if no one ever reads it. Celebrate the fruit of your labor, even in private if you have to, and know that just completing a polished work that makes you proud is a great accomplishment in itself. Share the things you are proud of with the world, knowing not everyone will share your enthusiasm. It's just like dating: not everyone is going to be attracted to you, but you might reach just one person and make them happy. That's worth the effort.
Little details that make a big difference:
Don't do what Stephen King does and force yourself to write a thousand words a day. Write when you want, but commit to your writing time, even if you don't produce as much as you'd like. Only implement a strict schedule if you get the sense that your work is worthwhile and productive. If not, refer back to points 3 and 4
Get your writing space in order. For me, it's a desk with no clutter, a few candles, and an expensive pair of headphones to block out the noise. My wife knows to leave me alone during that time. I recommend maintaining a playlist of music that inspires you to write. For me it's atmospheric horror music by Akira Yamaoka, fantasy music by Jeremy Soule and Adrian von Ziegler, or ambient electronica like Amethystium. Maybe for you it's sitting beneath a tree in your yard with your laptop
Keep your notebook by your bed so you can jot down middle-of-the-night ideas and get them out of your brain so you can return to sleep. You'll spend more time writing and less time pondering later on
Pre-writing rituals are a good thing. Clean your house, take your shower, eat something, etc. Do what it takes to ensure no other invasive thoughts distract you from your writing time
Don't share your work before it's finished. One negative comment can throw your entire project into question and make you wonder if it's worth finishing. If you're anything like me, getting tripped up by a negative response usually is a death sentence on the whole story