Best suggestion is leave gauze bandage on for at least 12  hours. Remember you just had hundreds of tiny needle pricks pushed into your skin, so treat it just  like you would  an open wound. Keep it clean, clean, clean!! You want to protect it from bacteria and all that other nasty stuff. 

The unveiling....Carefully remove the gauze bandage and tape. If you start to get some stickage use a tiny bit of warm water to remove. DON'T RIP IT OFF!  

Put some mild unscented soap in the palm of your hand  (Do not use a washcloth). Gently and carefully cleanse the area, and pat dry.

Apply a small amount of antibiotic ointment on the tattoo to protect from bacteria.  You don't need to slather it, a small thin coat will do. Repeat applying the antibiotic ointment 3 times a day for 3 days.

As it heals you will experience itching. If the itching gets to unbearable apply a bit of unscented lotion. DO NOT SCRATCH IT! Healing usually takes 7 to 10 days, depending on the size of the tattoo. As it heals you should get some sunburned skin like peeling. Try and resist helping it along. If you peel up a spot that isn't ready to come up you can cause scarring on your wonderful new tattoo.

One last piece of advice...SUNSCREEN! If you want your tattoos to stay with you for a long time, do them a favor and protect them.