Familiarize yourself with different styles of graffiti. No matter where you live, you can probably find graffiti nearby. If you can't find any in your neighborhood, visit a city if possible and look there--graffiti is predominately an urban art form. If a trip isn't possible, look on the internet. There are hundreds of websites that have pictures of graffiti; you can take a virtual tour of styles from across the country and around the world. Some pieces are obviously better than others, but the more you see the better you'll know the characteristic styles of graffiti.
Write down a name on a sheet of paper. You can start with any word, but your name is probably the best choice. Almost all serious graffiti artists start by developing a unique way of writing their names. As a beginner, it is probably easiest to print the letters and write in all capital letters. Use a pencil, and draw lightly so it is easy to erase anything you don't like. Leave plenty of space between the letters; you'll expand the letters to fill in the space later. Make them big enough to work with, but not so big that it will take forever to complete the graffiti.
Choose a style you'd like to use for the name. Bubble letters are especially popular in graffiti (see the related wikiHow for instructions), but there are plenty of other styles, too. You can have rounded edges or sharp, equally sized letters or some big letters and some small, etc. It's easier to emulate a style, and it's a good idea to have a picture of a graffiti piece in that style to refer to. Once you learn the basics you can develop your own style naturally.