How to get creamy out-of-focus backgrounds (beginner)

Contrary to popular belief, a large aperture is not required, nor is it the most important factor in order to achieve those pleasing creamy out of focus backgrounds to make your subject shine. For example, photographing a portrait with an inexpensive 55-200 mm f/4.0-5.6 telephoto lens at 200 mm and f/5.6 will get you  a nice blurry background, while a 8 mm fisheye at f/3.5 (i.e. larger aperture) will get everything in perfect focus between 0.5 m and infinity.

A long focal length (telephoto) and focusing at short distance from the lens are more important than large aperture. The all-blurry backgrounds of macro shots at f/11 are another example.

Therefore: Use the longest focal length available or practical on your equipment. Be as close to your subject as possible, and find a background that is as far away as possible from the camera. Then use the largest aperture (smallest f-number). Using this advice, it is even possible to get blurry backgrounds with a cell phone camera.
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Stay curious and keep practicing! /Sven