Care During the First Week:
Care is pretty simple after the first week. You do NOT need to re-bandage the tattoo. In fact, that would simply prolong the healing time -- and risk scabbing and loss of color if you are applying a gauzy type bandage (they tend to "stick" to the skin, and promote the creation of thicker scabbing on the Tattoo).
Instead, simply moisturize the Tattoo lightly with a lotion -- no more than 2 or 3 times a day.
Moisturize with a fragrance and glitter free lotion for first 2 or 3 days and gently massage a small amount into the tattoo. IMPORTANT: DO NOT SLATHER YOUR TATTOO WITH ANY CREAMS OR LOTIONS! Doing so will cause the skin to pucker, scab more heavily and almost certainly result in loss of some pigment. It is sufficient to lightly moisturize the skin when it "feels" dry, which will help with itching & scratching.
That said -- everybody's skin IS different -- use the above as a guideline, experiment and stick with what works best for you.