Get a concept. Open a notebook and outline a history for your superhero. Write down your superhero's physical and personality traits. Determine where your superhero came from, what his or her powers and limitations are, and who they "really" are. Name your superhero. Most names connect with the superhero's background or powers. These things will help you determine several things about your superhero, including costume, villains, and the overall direction of the story. Also, think about the motivation your hero has that drives him or her to fight crime. Spider-Man lost his uncle to a street thug he refused to stop for the police. That was the catalyst that sent him into the world of crime fighting.
Do a few rough sketches. You may design a costume using inspiration from a combination of your favorite heroes. You want to create a character that has the appeal that some of the classic superheroes have without getting too close to something that's already been done. Use a pencil for these rough sketches and draw as many possibilities as you can.
Settle on an idea and refine your superhero. Decide what colors you're going to use on the costume. How will you balance the look of your superhero when he's in costume and when he's in the role of his secret identity? Do a fully realized drawing of your character in each role. Use good quality sketch paper and color pencils to render the drawings as close to finished as you can get them.
Work on other characters to compliment your superhero. You need one or two super villains that have powers of their own, or the smarts to figure out how to hurt your superhero. Giving your superhero a weakness is important to the overall story. Even Superman has his vulnerabilities.
Use computer software such as Movie Magic Screenwriter, Microsoft Word or Adobe Photoshop to create a test-run comic featuring your superhero. Draw a simple three or four page comic and bring it into one of these programs so you can format your comic in panels. When you're finished, you can save your comic as a PDF file, or print it out and staple it together for a hard copy comic.
Publish your hero in a comic book. It's tough to try and get a major comic publisher to look at your work unless you attend a convention and present your work to them in person. Marvel and DC comics both work this way. There are countless smaller independent comic publishers you could contact. Look at the publishing information on some of your favorite comics or check an online database for comic publisher contact information (see resources). You might also consider publishing your own comic, then ask comic shops to carry your title on consignment.