Find a tattoo artist in your area, either online or by word of mouth, and make an appointment over the phone or in person. Always check an artist's portfolio before enlisting him for a tattoo.
Instruct the artist as to how large you want your sleeve to be. Allow her to measure the applicable portions of your arm either with a measuring tape or by simply wrapping your arm in paper and marking how large the design needs to be.
Instruct your artist on the designs you want tattooed and their style, and make an appointment to tattoo the line work.
Return to the shop at the specified date and time. The artist should have the entire sleeve drawn, but only a portion of it stenciled. This is because, depending on how large the sleeve is, it will take multiple sessions just to do the line work. It may take only a single trip for a 1/2 sleeve, but 3/4 and full sleeves can take 3 to 4 sessions.
Make an appointment after each line-work session for the next until all the line work is finished. The sessions should be about 2 weeks apart so that each portion can have plenty of time to heal.
Continue making appointments separated by about 2 weeks for shading, color and highlights until the entire sleeve is finished to your liking.