PROGRAMS USED:
GraphicsGale: This is the recommended program for this tutorial as it contains tools which are ideal for pixel art and drawing lines.
Alternatively MS Paint, The Gimp, or Photoshop can be used.
TUTORIAL:
In this tutorial you will learn about the best ways of drawing lines and creating smooth circles.
Simple Lines
When you are creating pixel art it's important to draw smooth looking lines. Smooth clean lines help to make your art more defined and generally look better.
In the diagram below you can see some of the more commonly used lines in pixel art:
As you may be able to tell, these lines are consistent in the way they are drawn. For example the 1:2 line draws 2 pixels for every 1 pixel across. The best way of drawing these lines can be with the line tool in your graphics program. However, you may have to edit the line slightly using the pencil tool to make the line perfectly even.
Below are some examples of simple shapes which can be produced using these lines:
The last 2 diamond shapes are typically used for isometric drawing where it's especially important to keep the lines looking smooth.
When drawing using lines to create an outline for your pixel art, it is often best to keep the outline to 1 pixel width. This ensures the artwork remains clean.
Circles
Circles are one of the harder shapes to draw in pixel art. Below you can see some examples of tiny circles ranging from 1 pixel diameter to 12 pixels diameter. 
To draw effective circles it is important that each quarter of the circle is the same. This ensures the circle is symmetrical. This can be seen the diagram below for circles of diameter 10, 11 and 12 pixels:
Now for an example. Using the different lines and circles we have learnt in this tutorial we can produce a clock face like the one below:
As you can see, circles are used for the outside edges of the clock. Different style lines are also used for the clock hands. Also note the 1 pixel width of the outlines which helps to keep the drawing looking clean.