Leave that bandage alone! A tattoo is a wound, and it needs to be cared for as such. Your tattoo artist should have put a bandage on your tattoo, and that bandage needs to be left on for two hours (at the bare minimum.) Listen to your tattoo artist; they may give you special instructions!
Wash your new tattoo. After you remove your bandage, use some lukewarm water and very mild soap to wash off the area covered by your tattoo. You need to remove any blood/plasma, ointment, oil or dirt from the area and make sure it is completely clean. Then gently pat it dry. Make sure you use a VERY clean towel to blot the area dry.
Rub some lotion on the area. Use a very light application of any non-scented lotion.
Scabbing and peeling is normal. Apply soft, moist compresses to the tattooed area a few times a day for five minutes at a time to help the scabbing go away.
After it’s healed
Make sure you use at least 30 SPF around your tattoo when going out in the sun.
Make sure you do not soak a new tattoo in the water when showering or bathing. Avoid submerging the tattoo in water for two or three weeks.
Surface Piercings: Make sure to wash your new piercing two times a day with saline, a mild soap or sea salt spray.
Oral Piercings: Make sure to wash your new piercing three to four times a day with Biotene.
Do NOT change jewelry for at least four weeks.