Familiarize yourself with the world of the X-Men. Ideally, you should read as many of the comic books as you can (compilations can be purchased at most bookstores or sites such as Amazon.com). Even the "X-Men" movies or the various animated series can help you get a feel for their universe.
Come up with a basic idea for a mutant superhero: his power, his nickname, his real name, his physical appearance and the kind of costume he might wear. Keep in mind that mutant powers aren't always beneficial and can be as much of a hindrance as a benefit.
Flesh out the character's background. What was his childhood like? Did his mutant powers manifest at birth or while he was a teenager? What kind of impact did they have on his life? How did he get into contact with Charles Xavier and The Xavier Institute for Higher Learning? The events of his past have a huge impact on which kind of person he becomes and how he interacts with other characters in the Marvel universe.
Develop the character's personality, based on the background you have created for him. Is he noble and righteous? Sullen and bitter? How does he get along with the other X-Men? Because he's at Xavier's school, he's generally on the side of right, though a number of X-Men (such as Wolverine and Gambit) shade their heroism with considerable moral compromise.
Write down an overview of your character, including his powers, weaknesses, physical data, history and personality. That way, you have it all in one place and can refer to it if you want to write a story or play in an RPG using your character.
Draw a picture of your character if you are so inclined, or use an online resource such as HeroMachine to do it for you.