A new tattoo is an injury to your skin. It's a lot like a scrape.
Typically, when the artist finishes, he or she will cover the new
tattoo with some sort of bandage. In the old days, this might have 
been gauze, but now we have non-stick bandages that are much better.
Some will use clear plastic sheet, such as Saran Wrap (TM).  This is
all right, and has the advantage that you can look at your new tattoo
without having to lift the bandage.  The bandage is largely to protect
the tattoo and your clothes, since new tattoos ooze a lot. Also note
that tattoos will ooze ink along with the other fluids, and it is not
unusual to find an imprint of your new tattoo on the inside of the
bandage with you take it off. This is normal.  Also, it is normal for
the oozing to go on for about 24 hours.

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