For the first few days, you should put A&D ointment on your tattoo, three times a day. After that, you can switch to a frangrance free and gentle lotion like Lubriderm, Aveeno, or Curel. Even vitamin E oil can work well for you.
Whatever you use, it should be without frangrance and be hypoallergenic. Your tattoo artist will have recommendations for you.
For more information on tattoo care, see the other FAQs on 'How To Take Care of Your New Tattoo.'