Purchase some paper and make sure you always have it with you. Artists always have paper because they might get inspired when out and about. You can then draw designs whenever inspired.
Think of a name you want to have to sign off your work. If you want to be an original graffiti artist, then think of an original name. You will then sign your name at the bottom or beside your work.
Practice sketching as much as possible. Sketch for at least three months before you start doing real graffiti on public places. You will want your designs to be perfect. Make your street art designs unique and an extension of your personal style.
Buy some permanent markers, stencils and other drawing mediums. You can even use stickers to make your designs. Find a place to do your first real graffiti design. You can do your design in a variety of colors, designs and textures.
Choose areas that are not completely public, but somewhere off track like in alleys. Graffiti artists do not want to get caught doing their art in public as they could get in trouble.