How to improve my photography skills with my Nikon D40?

As I asked about getting a new Nikon camera, but they had said to learn to use some new skills of photography. I really like the focusing of an object/person, and then the background area will be blurried. I just want that to be enhanced.

What you describe is 'Depth of Field'.It's not an especially difficult thing to learn you just need to understand how aperture works.

Practice by framing an image and focusing on a single point within the frame. You will need a large aperture to put that into focus and the rest of the image out.

Really all you need to do is go out and practice.

There are two things you can do to start

1) learn how to balance the cameras ISO, shutter speed and lens aperture to get exactly the shots you want.

http://camerasim.com/camera-simulator/

2) learn how to compose your shots so that when you press the shutter release, most if not all your images are brilliant.

http://photoinf.com/General/Robert_Berdan/Composition_and_the_Elements_of_Visual_Design.htm

These two things will help you a lot when increasing your skills.

The most difficult skill will be learning how to "see" and "read" light.

When you view others amazing photos, try and determine how they used light to make the images so compelling

Practice, practice, practice. Taking a photography course is always helpful, even 'old pros' sometimes forget the basics and could use a refresher course and to see what the latest innovations are. A good photo book (The Joy Of Photography) can also be really valuable. As for the specifics of your question you just need to practice using the aperture control(s) on your camera until you get the basics of depth of field and the relationship between the lens focal length, the lens aperture and the subject distance.

Hope This Helps.
Good-Luck!

You improve your photography skills in the same way you improve skills in anything. Education and practise.
Learn your camera and its controls - read the manual properly
Learn the basics of photography (exposure, composition etc) this can be done on your own with books or by taking courses
then practise what you are learning.

There are no magic settings, there are no shortcuts and there's no magic camera which will suddenly transform you from bad/average to good.

It takes a long time to become a good and skilled photographer.