There's hardly room for more than a few marks when you're drawing
an emoticon face. It has to fit easily with a line of text. Believe me, you won't have room for the Sistine Chapel in the common size of 15 x 15 pixels. Copy and print the graph paper grid below, and see just how expressive you can make your own emoticon.

Draw your facial expression first, then fill in the squares behind the lines to create a mosaic. There are so few pixels that it should be pretty easy to copy the result into an art editor on your computer.
Don't forget that each square on the grid represents only one pixel on a computer screen or phone. Even if you can triumphantly fit in lots of busy detail, it won't show. I managed to add a dot or two to Spotty here -
- but you probably can't see them, even though I was working at the enormous size of 16 x 16 pixels!
Why aren't emoticons the same size as favicon icons, the nice round number of 16 x 16 pixels?
Who knows, but I can tell you something I've learnt from experience. When you get down to this tiny size, a nice round number doesn't necessarily make a nice round face. You've probably noticed your face has a central protruberance known as a nose. When you're strapped for space, every pixel in a micro-portrait counts. If you draw a face 16 pixels wide, even a two pixel nose can seem too intrusive. On the other hand, a one-pixel nose unbalances the other features. One side of the face must be wider than the other.
If you don't want to bother with the graph paper, you can always draw your smiley directly on your computer.
Open Photoshop, Photoshop Elements or whatever art editor you happen to have. Most art editors have similar sets of tools.
Create a new canvas 15 pixels square.
Magnify your image several hundred times so you can see what you're doing. (This won't alter the actual size of your graphic, just what you see on the screen.)
Set up a one-pixel pencil.
Draw your emoticon face.
Drawing on a computer, you can work at a comfortable scale, while repeatedly zooming down to actual size (100%) to monitor how your emoticon is shaping up for its debut in real life.
Drawing an emoticon face directly on your computer has another advantage. It's easy to erase expression lines that don't look right, while keeping the ones that do. Sad, happy, sceptical, triumphant - whatever emotion you're aiming to express, you can chisel away at your image until you get the expression exactly right.
Satisfied? Save your picture as a GIF.