All of us dream every night, even though most of us remember our dreams only occasionally, and some people never remember any of their dreams. Similarly, inspiration is potentially available to all of us every day, but most of us remain uninspired most of the time.
There is a well-established technique for remembering more of your dreams. If you pay attention to your dreams, treat them as something important, and write down the dreams you remember, you will soon remember more dreams in more vivid detail. Even people who don't remember their dreams can get this process started by starting a dream journal and writing down any fleeting images or emotional tones that they wake up with, just on the chance that those impressions might be from a dream.
Just by paying attention to your dreams and treating them as important, you can quickly increase the number of dreams you remember.
If you want to have more inspiration in your life, one way to do it is to keep an inspiration journal. Make note of anything that even vaguely smells like inspiration. Write down ideas that tickle your fancy. Record any thoughts that start with "Wouldn't it be cool if..."
It's important to understand that writing down an idea is not a commitment to follow through on it. There will always be too many ideas and too little time. And it's just as important not to send away any inspiration just because it isn't practical.
For example, if after seeing the movie "Up" you think "Wouldn't it be cool if a rock band's tour bus were carried from city to city by helium balloons?" don't dismiss that thought because the engineering is impractical and your band isn't ready to tour anyway. You don't have to invent a new flying machine -- just acknowledge the inspiration in some way, perhaps by drawing a little sketch of the flying bus in your journal.
If you accept and acknowledge every bit of inspiration that comes your way, you will soon be visited by more inspirations, bigger and better ones, and some of them will be practical ideas that help solve your specific problems.