A great handheld technique is panning. This involves shooting at a slow shutter speed while tracking the subject with your camera, so you keep your subject more or less sharp, while blurring the background to capture a sense of motion. To begin with, use the following shutter speeds as a guide, then slow them down as your skills improve.
Motorsport racing: 1/250 or 1/500sec
Horse-racing, cycling: 1/60 or 1/30sec
Joggers, kids on bicycles: 1/30 or 1/15sec
To take a panned shot, pick up your subject in the viewfinder as it approaches, using Servo AF to keep it in focus, track it until it’s opposite you, then trip the shutter – but keep panning as you do this, for a smooth effect. Good panning is a tricky technique so practise, and don’t worry if your first attempts are a little bit blurred and jerky – you can produce great panning shots even when your subject is blurred as well as the background.