Practice on paper first. Most artists start with their names. Start with a pencil and play around with it. Templates can be easily procured online if you're uncomfortable free-handing bubble and 3D font.
Graffiti typically uses overlapping lettering. Try using a bubble font: vary between rounded edges/angles or sharp. A 3-D effect can be attained by using a darker color to shade the outside area of one side of each letter you write.
Don't feel constricted to the alphabet. Even to your name you can add character and personality through creative use of symbolism: speech bubbles, small caricatures, objects to replace letters in a word (for example, the image of a life preserver instead of the letter "O").
Trace over your penciled lines with black. Finally, use shading and lots of color. Use a fine-tipped utensil first, then shade using a thick-tipped tool such as a marker.
Keep practicing and looking at work that other graffiti artists have done. It's the primary way to learn and improve! As you move to a larger (and possibly outdoor) arena, you can replace pencil sketches with charcoal and chalk, and use a variety of spray paint to add color and permanence. Brushes and rollers can be used as well. Start with lighter colors and work up to darker colors. Varnish can also be thinly applied after the paint dries to ensure permanence.