Now it's time to take the shot. As I've mentioned, you want to follow the subject as it passes in front of you, so start tracking it through the viewfinder when it's well off to one side. Pivot your body as it approaches, and gently press the shutter release as it makes its closest approach. Don't "stab" the shutter--press and hold it to minimize any jiggling. And all the while, keep pivoting your body even if you can no longer see though the viewfinder, keeping the same pace you had before. Think of this like the follow-through common in any sport in which you hit a ball with some sort of club or racquet--tennis, golf, baseball. Whichever sport works for you.
After you take the shot, check the LCD to see how you did. Try to hone your technique until the subject is razor sharp and the background is a breakneck blur.
Finally, some post-processing never hurts. You might want to apply a little sharpening or clarity to the subject, but sharpening the whole photo will add ugly artifacts to the blurry background. So compromise: Use a selection tool like a magnetic lasso (in Adobe Photoshop Elements, that's in the sixth cubby from the top of the toolbar), and isolate just the subject. Lightly sharpen it by choosing Enhance, Unsharp Mask in the menu.