Most of the aspiring authors I talk to always mention the same thing. There just isn't time to finish what they started.
I would say that I have written for quite a few years, but only just recently started to feel like I was really getting somewhere. Have I become a published author? No, not quite, but I do have quite a few small works completed, and a few novels already through their first or second edits.
Perseverance is not a long race; it is many short races one after the other. -- Walter Elliot
Although there are tons of things you can do to increase your productivity, or finish a writing piece faster, I only have one suggestion.
Create Short Term Goals
Life is crazy, so setting a small, attainable goal, or even an ambitious one, gives your dreams substance. You could try out NanoWrimo (national novel writing month) where you measure success in adding to your word count. Or you could go for a certain number of hours you want to write in a month, and keep track of your time every day you write. You could decide to write one poem that day, just to have something completed for a change, or focus on a short story in a week.
There are tons of sites that focus on an open platform to share your writing with the world, and many of these places have built in challenges or "word sprints". Try one of these methods out to see how they work, because I am glad that I did.