Use a paring knife to cut around the center of the avocado, lengthwise. Rotate the avocado around slowly to move your knife completely around the pit until you have two clean halves.
Hold the avocado half that contains the pit gently on your work surface (not in your hand!), and use the knife to remove it. With a bit of force, start with your knife slightly elevated and chop into the pit. Then gently lift the knife, twisting it a bit, and the pit should easily come with it. Use a towel to remove the pit from the knife (not your bare hands!).
Place both avocado halves round side up on your work surface. Cut about ¼ inch off of each end.
Use your hands to gently peel the skin off the avocado. (If it doesn't come off easily, you can use a spoon to scoop it out -- all in one piece, if possible.)
Round side up, slice the avocado to the desired thickness. From there, you can also cut it into any size dice you'd like. (Avocados are slippery — to keep the slices intact, use a flat-bottomed spatula to move them to your serving plate or to the dish you’re adding them to.)