There are some who say to always write down your ideas. Others say just let the ideas simmer and the best ones will stay. Personally I've done a combination of both. I've written ideas down and found they've fizzled out while others stay put. Then there are thoughts that develop and I never write them down but they continue to grow.
So I believe it is something that is an individual choice. Experiment. Find what works for you and stick too it. Ideas are wonderful, even those that don't really work. You just never know when something will.
Now where to get ideas. Prompts are fabulous. There is a wonderful podcast called Writing Excuses that ends each session with a writing prompt. (http://www.writingexcuses.com/) They have crazy, wacky prompts but sometimes those are the best ones. (They also have wonderful writing tips.) Pick random words and figure out how to work them together. Grab a postcard or picture and write a story about it. Take different situations and play with those. Take a look around you, something is bound to jump out of you. Just take a chance and see what happens from there.