It is absolutely possible to throw the background using your kit lens. In a nutshell, use the largest focal length, with the most wide open aperture (remember that f-stops are measured in fractions [f/2 is larger than f/8]), position the subject as close to the camera as you can for the framing you want, and keep the background as far away behind the subject as you can. The further the background is behind your subject, the blurrier it will be.
That being said, in the quest to blur the background, bigger is better. So, keep in mind that it is possible to blur the background with an 18-55 shooting it at 55mm and it's most open f/5.6...but you'll get more blur using a 50mm f/1.8 prime and shooting it at any f-stop more open than f/5.6.
From your question, it sounds like you may also want to check out some exposure tips.
If you use Aperture Priority mode and set the camera to the largest aperture, it will pick the shutter speed for an appropriate exposure. If the chosen shutter speed is too slow, you may get some blur due to you minutely moving the lens. In this case, you'll need to increase the ISO.
Keep in mind that increasing ISO increases noise, so in general, you want to use the lowest ISO possible.