• Do not re-bandage the tattoo.
• Do not apply Vaseline, lanolin or petroleum based products.
• Do not apply alcohol. (Some lotions have alcohol in them. Why, I have no clue, but it burns like hell on a fresh tattoo.)
• Do not rub, scratch or pick at the tattoo.
• Do not expose the tattoo to direct sunlight, swim or soak in sauna, steam bath or bathtub for two weeks.
• Be sure clothing touching your tattoo is clean and soft.

A tattoo is considered minor surgery (that's a much nicer way of putting it). It may bleed a bit at first but it will stop within a couple of hours. Most artists recommend the tattoo be kept bandaged overnight or for at least two to five hours. If the gauze sticks to the skin, soak the area with cold water until the gauze loosens, then remove carefully.
Once the tattoo is exposed, wash it carefully in cold water, gently applying antibacterial soap with fingers (never use a cloth) to remove all surface blood. Rinse with cold water, pat dry with a clean towel, and air-dry for 15 minutes. Then, gently and sparingly apply a thin layer of triple antibiotic ointment. Repeat 3 or 4 times a day for 2 to 4 days.
After 5 to 14 days, the tattoo may start to peel (this is normal like a sunburn) and scab. DO NOT pick or peel the skin away (duh). Let it fall off naturally during washing or application of triple antibiotic ointment. Fresh skin will soon replace the dead skin. Colors may fade during the process, but will return when healing is completed.
Triple antibiotic ointment and lotion keep your tattoos from drying and the skin areas soft and moist. Always apply sparingly. Too much prevents the skin/tattoo from breathing, and can cause leaching of the colors. If this happens, discontinue use, wash the tattoo, pat dry, and consult your tattoo artist at your earliest convenience.
After a few weeks, all scabbing will be gone, but the area may still be sensitive. Continue regular cleaning and application of triple antibiotic ointment or lotion, for proper aftercare of your tattoo.
Exposure to the sun is the major cause of tattoo fading, but after a few months you may sunbathe in moderation. Always use a sun block (at least SPF-30 sunscreen that provides UVA and UVB protection).