You want to manipulate the depth of field. This is the area that is acceptably sharp, just in front of and just behind the plane in space where focus actually is. Three things control depth of field... aperture, focal length and distance to subject. To get a shallow depth of field you want a wider aperture (that means a smaller f/stop number) you want a longer focal length and you want to be close to your subject. Now it's often not possible to get all three of those things, so we just go with aperture and whatever else we can. Since aperture is the biggie and the easiest factor to alter in most situations.
Other things will affect the perception of depth of field. Keep your subject separated as far as you can from the background. Depth of field will seem larger, meaning more will look sharper, with smaller sensors like your camera uses. It will also seem larger with smaller prints.
You will have a tough time getting shallow depth of field shots with the camera you have. There's a lot of factors working against you. But it's not impossible so read up on how to control the aperture with your camera and play around.
