Watch the world around you. Take in the subtle details the average person may overlook. Don't wait for a moment to come to you. Seek out those moments that not only stand out and mean something to you, but moments you feel might speak to others as well. Moments can be as obvious as a hawk flying through the clouds or a child trying to finish an ice cream cone as it runs down her arm. People watching is ideal for writers trying to capture body language and other behaviors in writing.
Carry a camera or a notebook with you. Be prepared to capture a moment whenever it occurs. If you're a painter, it will be hard to carry an easel and paints, but you might carry a sketch pad to capture the general idea of a moment and recreate it later. If you're a photographer, you're lucky. You can carry your tool with you at all times. For a writer, a pencil and notebook can help you capture behaviors and events you might use later.
Recreate your moment through a chosen medium. Sit down to work in your creative space and examine your photograph or sketch. Read the words you wrote to remind you of the details of what you saw. Ask yourself how you felt when you witnessed the event and what details stand out to help you recall, then paint or write and recapture the magic.
Capture the moment using the best tools of your artistic medium. A painter might remember the color of clouds and use a particular blend of paints to recreate it. A painter might choose to capture a facial expression with minimalistic brush strokes as opposed to detail, capturing only those elements that define the expression. Writers might combine several notes made about different people to create one individual in a story. The photographer might choose a black and white setting or even a micro lens for capturing details such as water drops on a flower petal so close the inspiration may be to try and drink them. Whatever method, always use the approach and tools you feel will complement the moment you want to remember in your art.