If you haven't watched it, "Six Days to Air," the South Park documentary, is a must-see for any artist. What these guys accomplish in six days is incredible, and their processes are not magical or fantastic - anyone can work as hard as they do. Thankfully, we just don't have to. Not quite as thankfully, we don't make nearly as much, at least not yet.
There's one specific line that really struck me, and it seems so simple now that I have heard it. Trey Parker, if you don't know, is the sole real scriptwriter for South Park. The other "writers" on the crew are basically just idea-men (and women) who whip up funny ideas and help make a generic structure, and then Trey sits down and writes the full script himself. And he says at one point, while writing a script to "go through your story, find all the ands and change them to buts and therefores. If all your ands are buts and therefores, you'll have a much better story."
What does he mean by saying this? Simply, make things happen for reasons. Don't just have your story be "Mary was captured and then she escaped and then she went to Kamchatka."
Instead, have it be "Mary was captured, but one of her captors turned out to be a longtime fan of her slam poetry, therefore he helped her escape, but they were caught escaping therefore Mary had to find the nearest way to escape which was a barge headed for Kamchatka."
Buts and Therefores require action. But needs something to oppose your intended action, and therefore needs a reason to exist. They're automatically deeper than "and," and will bring more to your story than the humble conjunction.
Read through your story. Mark down the "ands." Find the areas where things just happen, not happen for a reason. This doesn't mean coincidences are bad - not everything has to have a specific reason to occur, but more is better. And remember that golden rule of coincidences in writing: It's great for your characters to get into trouble because of a coincidence, it is bad for them to get out of trouble because of a coincidence.
When you've found your ands, see what you can do to make them buts or therefores. What clues have you given in your story that you could tie in? What side character's backstory would apply to this scenario? How can you use that oblique reference you forgot to mention again later? (we've all been there before)
Remember, as the author, you're a god. You are omniscient and omnipotent. The smallest things can come together to cause the strangest events to occur to your characters. Don't be afraid to be crazily imaginative. The worst you can do is be boring, and just say X happens, then Y, then Z.
Do you know of any Ands you would have liked changed to Buts and Therefores in movies or books? Any leaps of faith that just felt a little too far? What would you have done differently to make the sequence have a reason or more solid grounding in the backstory?