Wash the fresh tattoo in warm water, at least three times a day, for the first two or three days after you get the tattoo. Use antibacterial soap and a clean towel for each washing and never rub the tattoo for any reason -- just dab the soap and pat the towel.
Apply a thin layer of protective ointment, such as Aquaphor, Burt's Bees or Neosporin, to the tattoo after each cleaning for the first two to three days.
Continue to wash your tattoo at least three times a day after the first three days, but switch to cold water. For a regular tattoo, you would always use warm water, but hand and finger tattoos are much more susceptible to any level of heat.
Stop applying the protective ointment after the first three days and instead apply nonscented hand lotion. Hand lotion, which is usually lighter than an ointment, will allow the tattoo to breathe, helping the skin heal. Most nonscented lotions don't contain alcohol, which can leave your skin too dry.
Continue washing and applying ointments and lotions for at least two weeks until the tattoo is healed.