Open up the art program of your choice. Most software have a standard set of tools. Focusing on small emoticons, your basic aim will be to draw circles and ellipses, use coloring for faces, keeping in mind the size. The latter is an important consideration given that you will be inserting emoticons in the middle of the text.
Set the appropriate dimensions i.e. the canvas size must not be more than 20 by 20 pixels. It is recommended that you set the pencil size to one pixel to give yourself room to add details.
For clarity, zoom in your canvas as much as you want. However, for precision, revert to the original scale and see how the emoticon looks in real size.
Now decide on the shape. This will entirely depend on you, whether you want to keep it simple (round shaped) or draw a more detailed icon. After you have the basic shape down, fill it with color before adding features.
For frown emoticons, blue, grey or any dull color could be used, if you are not comfortable with the bright yellow, which is mostly associated with happiness, joy etc.
Now work on the animation aspect of your smiley. This is the major advantage of computer programs. How will you associate sadness? In order to make an animated emoticon, you will need to make different frames, before the animating software will merge those frames. For instance, if you want your emoticon to walk with a teardrop pouring down; you will need to make specific frames which follow this sequence.
After completing your frown emoticon, save it as a gif image, which can be imported into several popular chat clients for use.