Keep the tattoo clean and moisturized, avoid direct sunlight and swimming, and follow any specific instructions provided by your artist.
If using Aquaphor or A&D always remember to wipe off any excess with your clean hand to avoid a poor healing experience.
If using an adhesive bandage such as Saniderm or Tegaderm:
So long as the tattoo remains sealed under the bandage it is safe and can be removed whenever you like. It is normal to see blood and ink under the bandage. Remove after sweat induced physical activity.