There's hardly room for more than a few marks when you're drawing very small graphics for an emoticon face or other diminutive symbol. Believe me, you won't have room for the Sistine Chapel in 0.0003 megapixels.
If you like to start on paper, print a few copies of the graph paper grid below for a some warm-up sketches. Enlarge the grid some more before printing if you like.
Draw your facial expression first, then fill in the squares behind the lines to create a mosaic.
Each square on the grid represents only one pixel on a computer, tablet or phone display. There's no room for lots of busy detail when you're drawing very small graphics.
Why have I made the graph paper 15 x 15 pixels instead of 16 x 16, which is the standard size for an old fashioned favicon icon? It's better for a tiny graphic of a face.
At this impoverished size, a nice round number does not make a nice round face. You've probably noticed your face has a central protruberance known as a nose. Every pixel in a micro-portrait counts. If you draw an emoticon 16 pixels wide, even a two pixel nose can look enormous. Reduce it to one pixel and it unbalances the other features. One side of the face must be wider than the other.
Working on your desktop, open Photoshop, Photoshop Elements, Painter, Art Rage or whatever art editor you happen to have. Most art editors have similar sets of basic tools.
Create a new canvas 16 pixels square.
Zoom up your image about 800 times so you can see what you are doing.
Set up a one-pixel pencil or pen.
Draw your small graphic. You'll probably find you now want to make alterations if you're copying from a paper sketch.
Drawing on a computer, you can work at a comfortable scale, while repeatedly zooming down to actual size (100%) to monitor how your symbol is shaping up for its debut in real life.
Drawing an emoticon face directly on your computer has another advantage over paper. It's easy to Erase or Undo expression lines that don't look right, while keeping the ones that do. Sad, happy, puzzled, crazy - whatever emotion you are aiming to show. Expressions do come across, even at this very small size. You can chisel away at your image until you get the expression right.
It is possible to try out various expressions on separate layers, but hardly worth it at this size.