Han Ping's 3rd response is so important. Once you move out of your area of expertise, you make discoveries but also create new partnerships, new synergies, new connections. Connect with people who view the world differently
Ask 'Why' and 'What if?'
Look for what is missing rather than what is there. Look closely at the spaces between things
Be playful, tinker with ideas, make mistakes, make messes take risks as Ian and Han Ping suggest
Be surprised by small things you observe or hear or touch
There are some techniques for working with groups to elicit ideas, collect and organize them. There is an article in The Innovation Journal (www.innovation.cc) in its early years about this.
IDEO is a company in California that has lots of experience in creativity and innovation. They work closely with Stanford and there is free online training in "human centered design."
Systematic Inventive Thinking is a firm in Israel that teaches innovative thinking by thinking INSIDE the box. It is sometimes too difficult to think about ALL the possibilities while focusing on something closer at hand is more productive. Think of the creativity used on Apollo 13 when they could only use the supplies on hand.
Improvisation in front of a group also creates difference ways of thinking. Sounds odd but it creates new pathways in the brain.