Well the quick and dirty way is to use the good old MS Paint 
Iām not an artist but I prefer Photoshop, it has dozen of unnessecary stuff for sprite creation but Iām used to it^^
One of my friends is using Pixen but it is Mac OS X only 
Quick Google search brings up this list: ://forums.rpgmakerweb/index.php?/topic/5027-software-for-making-pixel-art/
Regarding the creation of sprites, I usually start with some draft on paper, switch to PS to make the outlines, then base coloring + basic shadowing followed by finer details and finally better shadowing.
Exactly like this:
But like I said Iām not a professional artist so there might be better ways to do it^^