First question is ofcourse:"What kind of sprites do you want to make?"
If you want to create animated sprites, you will have to know a lot about the movement you're trying to recreate, so for someone who hasn't made them ever better to start simpler..
If you want static sprites, you could try using programs like paint, gimp or work with vectors in for example Inkscape..
Artwork could sometimes better be called Hard work, because creating something that is pleasing to the eye takes a lot of practice and hard work..
I want to make sprites more or less in this style
humanbalance.net/gale/pics/sample1.gif
It's just an example.
I know about handling a bit, the character design (how it is) I've already done it. I really do not know, it turns it into a sprite ...