The first step is to prime your eyelid. This is important to stop the eyeshadow from creasing and makes colours look bolder. I use Urban Decay's Primer Potion, however there are others you can use, like Too Faced's Shadow Insurance or MAC Paint Pots. I personally find the Paint Pots crease on me though. These products are on the expensive side, however I find they last me a long time and are invaluable for making my eyeshadow stay on and look how I want.
Spread a small amount of the primer over the eyelid from lashes to the browbone, and under the lower lashline.
Next, you will need a soft eyeliner pencil that you can smudge easily, or a dark cream eyeshadow or gel eyeliner. Something dark you can smudge around your eye. Put this onto the lid, keeping mostly near the lashline, and a little along the lower lashline. It doesn't need to be neat at this stage. You can use black, I'm using a dark brown as it's less harsh looking.
Now, blend the liner to soften it. You can use your finger or a stiff brush. Remove any stray smudges that get on your cheek or browbone with a wipe if necessary.
Next you will need a dark eyeshadow to set the liner. You can use whatever you like here really, you can pick something to complement your eye colour or keep it monochromatic. I'm using Hustle from Urban Decay's Naked palette, which is a dark plummy brown. If you like you can use a fluffy brush to blend out any harsh lines.
Just add mascara and you're done!