I don’t know about your camera, but my Nikon D7000 boasts 6 distinct autofocus modes for still photography: single-point, nine-point dynamic, 21-point dynamic, 39-point dynamic, 3D tracking, and Auto-Area. They are all there for a reason.
Most of the time, I use single-point for precise focus of stationary subjects, such as portrait models. I put the focus point on the near eye and shoot.
With moving subjects, things can get more complicated. Shooting dancers on a crowded stage, I generally choose nine-point dynamic and try to keep the focus point on a single dancer’s face. The autofocus system will track within a limited area around the original focus point, and hopefully will not get fooled by another dancer’s face or a particularly contrasty background element.
Recently I shot dance rehearsals featuring two dancers in a studio. In this circumstance, I became quite comfortable with 3D Tracking and AutoArea.
I rely on AutoArea when I’m using a super wide-angle lens and shooting with the camera away from my face, usually around stomach level. Since I cannot see through the viewfinder, I trust the camera to identify and focus on the nearer subject in the frame. The wide-angle lens provides considerable depth-of-field, so there’s a wide margin for error, and so far I’ve been very pleased with the results.
With longer lenses, I’ve been using 3D Tracking, which tracks the moving dancer across the entire frame after I lock focus on the dancer’s face or shirt.
It’s taken quite a bit of practice to determine which autofocus modes to use in which circumstances, but I’m developing a healthy respect for Nikon’s engineers. I often refer to the manual or Thom Hogan’s excellent guide, but experience brings the lessons to life, so get out there and experiment! You may find that a little-used camera feature is exactly what you need to nail the shot.