The blurry background is really a result of 'shallow depth of field'. The following all contribute to shallow depth of field:
- Focal length: The longer the focal length, the shallower the depth of field.
- Aperture: the wider the aperture (smaller number), the shallower the depth of field.
- Distance to subject: The closer you are to the subject the shallower the depth of field.
So, the 'tricks' are use longer focal lengths, get as close to your subject as possible, shoot in Av 'wide open' (the widest aperture the lens supports) and position yourself so there is maximum distance between your subject and the background.
Be aware some lenses (particularly low quality zooms) deliver poor sharpness wide-open. Prime lenses and quality zoom lenses lend themselves to this photo style very well. You need a lens that is relatively sharp at wide apertures.
Remember, backgrounds do matter, position yourself for the best possible background. This will make or break the photo.
These examples really show off the shallow depth of field possible with a full frame camera (Canon 5D) and fast, high-quality telephoto prime lenses. With a 'crop-sensor' camera (using the same lens) you would have 1.6X less 'blurry background.'