OK please note that I'm not the greatest spriter ever but I know a lot about spriting. But also note that this tut is mostly for all of those Sonic lovers that spam the blogs with minor Sonic recolors, naming them all Ultima and banning anyone who gives crits. But either way look at this because it took me a while to write this. And by the way, don't expect a TL;DR to this.
Step 1: The idea Before you make a fan character you have to take some time to think one up. Don't just take Sonic and make him black, that is an overused edit. Sometimes you might need to write down his/her qualities and maybe even draw him up before you sprite him/her.
Step 2: The name Now this is something that most spriters are annoyed by, unoriginal names. Don't, and I mean don't name your character the color of their skin. Seriously, "Purple the Hedgehog" I forgot who made that guy but come on. Also not everyone should have "the <insert animal's name here>" in their name. Try to think up an original name, names like Ultima or Darkness are not only overused, but it is horribly cheesy and does not sound as menacing or heroic or however you intend it to be.
Step 3: giving them a backstory No one really like corny, two page long monologues which end up relating to the main character of the story. Try thinking of something original.
Step 4: Actually spriting the thing Now I can't really tell you secifically how to make him/her, it's your fancharacter, you should try to make him/her look original. Just remember, if you're going to use some other character as a template it's ok to edit him/her as much as possible, recolors are hated by spriters, amateur and proffesional but edits, even if it's as minor as giving them a weapon is not as hated, as long as it looks good.
How to make a good recolor Now I don't condone recoloring but if you do decide to go "Feck off, Donga. I'm going to recolor anyways, you're not the boss of me." then if you're just practicing spriting you might need to take the colors, or palette from a different character rather than using the 28 colors MS paint gives you. If you want to take the colors from another character you must click the button over the pencil that looks like a turkey baster and click the color you want to use, then the pencil color will be changed to whatever color you cliked.
One last thing Take constructive criticism. I know you don't like to hear someone going "Hmm, it's ok but it needs improvement" on something you worked so long on but take the criticism, no matter how rude it sounds, it might help you improve.
I'll probably add more to this but this is all I have for now.