Capturing a Moment: Speed
Another strategy is to shoot a lot, and quickly, so that moments cannot escape. This is a way of working that became more popular when small cameras like early 35mm cameras were invented (35 mm cameras were often called "miniatures" because the film was so much smaller than the standard 8 by 10 inch view camera sheet film). These cameras were much more portable, and framing and focusing was considerably faster - allowing a photographer to keep up a continuous barrage of shots until they ran out of film. Now that many photographers use digital cameras, and camera memory cards are cheap and capacious, the number of photographs one can take is limited primarily by the speed of the camera's processor. The downside of this method of shooting is that an enormous percentage of the images will be unusable, and many could capture the moment you're looking for, but be badly framed, poorly exposed, or blurry.
Garry Winogrand worked in this way, and though some criticize his work for horizon lines that are not level, he captured so many intriguing moments that his images are still amazing. Winogrand, though, had hundreds of discarded shots for every few he kept.
Many documentary photographers adopt a strategy somewhere in between these two extremes. They take a lot of pictures, but each one is framed as well as possible under the circumstances. You'll end up with a lot of usable material and, with luck, a small number of the images will be outstanding.