1) Remove the saran wrap when you get home and gently wash the tattoo with warm water and unscented antibacterial soap (any unscented antibacterial soap will work).
2) Put a thin layer of unscented moisturizing lotion on the tattoo. Don't use antibiotic cream like Neosporin.
3) Repeat steps 1 & 2 for the next two weeks, 2-3 times a day.
4) Don't touch your tattoo with unclean hands, and don't let anyone else touch your tattoo while it's still healing.
5) Don't let your pets touch your tattoo, either, if possible.
6) For that matter, avoid going into the sun with your new tattoo for the first couple of weeks, if you're able to, in order to give your tattoo the best chance to heal. If you must go out in the sun, wear loose fitting clothing to cover the area.
7) Whatever you do, DON'T SCRATCH OR PICK AT THE TATTOO, NO MATTER HOW BADLY IT ITCHES. You may ruin the tattoo or worse, cause an infection.
8) If your tattoo becomes swollen, hot to the touch, or begins to leak anything other than excess ink and clear fluid ("plasma"), see your doctor.