When we draw with graphite pencils, most of us start with an outline. The problem with this is that objects don't have outlines in real life. For more realistic, life-like drawings, try challenging yourself to drawing without using lines. Instead look for areas of value; define the edges of your object with the contrasting values of the background and foreground, or by letting the edge vanish. Look carefully and trust your eyes. Sometimes subjects we think should be dark actually have a lot of lighter tones in them, and vice versa.
Having the right tools will make shading a lot easier. Make sure you have a range of pencils with different grades of hardness/softness. and HB pencil is good for midtones, while H pencils are harder and B pencils are softer. The higher the number before the H, the harder the pencil (example: a 4H pencil is harder graphite and makes lighter marks than a 2H pencil). The higher the number before the B, the softer the pencil is (example: a 4B pencil is softer and makes darker marks than a 2B pencil). Start off using HB for midtones and H for highlight areas, with B or 2B for darker areas. Having a 4B or 6B pencil is useful to acheive very dark values. HINT: don't be afraid of dark tones! Many beginners shy away from dark values, leaving their drawings seeming flat. Having a range of tones from very light to very dark, with midtones in between, will give your drawing depth and life.
For practice, visit the Luce Foundation Center for American Art and the Smithsonian American Art Museum during one of their weekly Sketching: Draw and Discover sessions. The sessions include a discussion of artists' sketches and time to sketch from some of the more than 3,300 objects on display.