Solving Problems and Creating Solutions

It's all good and fun to heap conflicts on our characters. That's what we want, right? The only problem with problems is that we have to solve them.

Two Birds with one Stone

One way to solve is by using one problem to solve another. You wouldn't believe how often this works.
For example, I was struggling with a Character A's lack of involvement in the plot. I was also trying to figure how Character B finds out that Character C is in trouble. The solution to both? Make Character A the messenger boy.
In these cases, the two interlocking problems aren't always obvious. Try combing through your story and making a list of plot holes and problems. Then put a couple together to see if they match up. It's sort of like a puzzle; two puzzle pieces are enigmas alone, but click them together and you're that much closer to the finish line.

The Brainstorm

This is the most logical technique; sit around and think brilliant thoughts. However, for most of us, it's not that easy.
Brilliance doesn't happen under pressure. Which is why the brainstorm shouldn't be taken seriously. If you're exerting pressure on yourself to be a genius 24/7, chances are you won't be.
Trust me. I once stressed and racked my brain for an hour, convinced that the only way to complete my book was by refusing to stop my brainstorm. In a word; failure. The only thing I accomplished was a week-long writer's block.
Successful brainstorming should be relaxed musing. No pressure, there's always another day to be amazing.

I never quite know when I'm not writing. Sometimes my wife comes up to me at a party and says, "...Thurber, stop writing." She usually catches me in the middle of a paragraph. Or my daughter will look up from the dinner table and ask, "Is he sick?" "No," my wife says, "he's writing something."
~James Thurber

Change the Facts

If the facts don't fit the theory, change the facts
~Albert Einstein

Sometimes, we write ourselves into a corner. The scenario is too impossible, the conflict cannot be resolved, and the characters are dead meat. If that's the case, un-write and rewrite. You're the author. Give the villain a tendency to oversleep, make the dungeon walls hastily built, the fortress located in an abandoned quarry, the evening wine drugged (You can imagine for yourself what these suggestions would resolve.)
You don't have to make things easy for the characters, just possible.