Why am I unable to take sharp photos with my 18-55mm lens?

It's my first DSLR camera (Nikon D5300), and the 18-55mm lens. I'm still taking pictures in auto, but I feel that my pictures are not as sharp as the pictures I see of my friends with other lenses.

You didn't provide enough information. That lens certainly is capable of taking sharp pictures, especially around the 18mm setting. Try a short exposure time, just to eliminate any motion blur you might be running into.

Step one, manual.
Step two, distance from camera. You only have so much focal length.
Three, camera shake.

1. Are you shooting in low light, like indoors? Since the shutter stays open longer in low light, any camera or subject movement, even slight, will blur your photos.

2. You are not using auto focus, or your auto focus settings in your camera's Menu are not correct. Read your manual on how to use auto focus.

3. Your lens is dirty, front or back. Or your camera's sensor is dirty (have a camera repair shop clean it -- not a DIY job for most people).

4. Possibly the resolution and quality settings in your Menu are not maximized for best quality. Read your manual for these settings.

5. What are you using to view your photos? If the software you're using to view your photos is reducing size or quality, your photos will appear to be less sharp when they are actually not.

That lens is capable of taking fairly sharp images. If you set your aperture to f/8, the lens will do pretty good. You also need a fairly fast shutter speed to reduce motion blur. 1/100 seconds, or faster, should suffice. You also need to hold the camera properly. If you're using live view, it will be hard to minimize motion blur. Motion blur is minimized when using the view finder and holding the camera properly. This is covered in your manual.

When I went from my D40 to D7000, the increased resolution of the sensor (6 megapixels to 16 Mp) really showed that my holding technique got lazy.

There are better lenses out there where the sharpness and contrast is noticeably better than the 18-55 lens. However, to see this improvement you need to have the proper skills to bring out the best. This includes holding the camera, composition, lighting, learning about depth of field, …

It's in the light. If you are indoors, light is low. Remember, the camera does not see exactly the way you do. When light is low (indoors, or night time outdoors) use flash.

Learn to shoot in manual. If you do, your photos will improve over time. The D5300 is a great camera, and the 18-55mm is a good lens. It is probably your fault that the photos are not sharp, not the gear's fault.

I would say because you don't know how to operate it or the camera properly. Squidmaster has a good idea. Read the manual. Learn about focal length and don't shake the camera.