The traditional way of shooting a scene: get a master, close-ups, two-shots, three-shots (if there's a multiple-character scene), and cutaways. These setups come from a shotlist and storyboards. It's a fine way to make a movie, but it's not the only one, and for low-budget filmmakers, it may not even be the best choice.
Firstly, storyboards, while very useful, don't always reflect reality. They make sense when you have very specific visuals in mind, and control over the location and cast. But if your cast wants to do something different on set, or you lose the location, or a big truck parks in front of that wonderful canyon view you were counting on, your boards will become useless.
Secondly, two of the historical reasons for shooting coverage don't apply to indie films: studio control and the expense of film. Studios liked directors to shoot coverage. If they didn't like the director's version of the film, they could re-edit it more easily. And film costs A LOT of money. If you keep a 35mm camera rolling for one minute to swing around for another angle, you've just shot $50 (roughly .58/foot in stock + processing + telecine * 90 feet per minute) of unusable footage.
The alternative is to use moving masters and 'swingles.' This term first came up during a feature I worked on as a production manager and 1st AD, where we had a lot of dialog-driven scenes featuring many characters, and a fairly brutal 8-page/day schedule. Rather than try to cover every possible angle between characters, we opted to start with a moving master that picked up some coverage. The DP then hand-held (or glidecam-mounted) the camera for singles and two-shots that swung between characters during the take. The camera favored a different person during each take, but swung to cover the others as necessary. The determination of who to cover when was based on the actors' beats, and on physical movement. Sometimes we let the camera roll, reset everyone, and started again, just to keep the energy up. After several takes, we had more than enough pieces to edit the scene together with.
When swinging around, you'll miss something on each take, but you can make up for what's missed on subsequent takes. Directors must really know their material, and everyone has to be on their toes about continuity. This technique won't work if your lighting won't allow for it. But the advantages are numerous. You can let the camera work around the actors rather than have the actors worry about the camera. You can cover a scene in a fairly short amount of time. Keeping the frame moving adds some eye candy to a scene. It also pushes you away from an over-reliance on close-ups.
You don't have to abandon traditional coverage, but this becomes another tool in your arsenal. Good luck and happy shooting!