Draw many ideas for your sign in your sketchbook. Legibility is less important than having a unique, easily identifiable design, so experiment with strange letter shapes and embellishments. If you haven't come up with your graffiti moniker, this is a good time to experiment with the visual shape of different words and spellings.
Practice your sign several times in your sketchbook until you've mastered the strokes and the movement of the marker. Work on executing the tag quickly.
Purchase spray paint. You can buy it either at a craft store, a home improvement store, or at a specialty graffiti store, many of which can be found online.
Find a wall to tag. Tagging constitutes vandalism which is punishable by law, so it's best to find a place you have permission to tag. Sometimes skate parks or bars allow people to tag their walls.
Spay your tag on the wall quickly and accurately. Repeat the tag as much as possible, in as many places as possible.