kidbuu gave a very good explanation.

If you're going to be printing your work then you should be setting your canvas size in inches/centimeters not in pixels. I would start with something like 6in x 6in and use a resolution of at least 300dpi.

as for the image you referenced. It looks like it was painted in photoshop. Many people paint in photoshop the same way you paint in real life, by using a device called a pen tablet.
See: http://www.youtube.com/watch?v=xJNvKjQHv8I
Pen Tablets: http://www.wacom.com/index2.php