A few months ago, I read Coraline by Neil Gaiman and the copy I happened to be reading included an interview. He noted that he would write 100 words of the story every day in order to get it finished, little by little. I think that is good to advice for anyone who has an idea for a story, but feels suffocated by a lack of time to clear their head and focus purely on writing their story.
Another good tip is to carry a notebook and pen with you everywhere. When I say everywhere, I mean everywhere. I cannot tell you how many times the perfect sentence has popped into my head while I was taking a shower or just as I was on the verge of falling asleep. Keep track of all your ideas big and small, no matter how trivial.