in my experience of tattoo aftercare, the freshly finished tattoo should be coverd with cling film for a few hours at least, your fresh tattoo will leak plasma (white liquid stuff) for about 4-6 hours after the tattoo is done (if its a fairly big tattoo anyway) after this time, dab with a soft cloth with clean warm water, not too hot because this stings like hell! then wait for aout 10 mins for it to dry before putting anything on it.
i have tried various different types of aftercare creams in the past but i have found none to be as good as tattoo goo, not the stuff in the squeezy tube but the stuff in the little round tin... it has my tattoos heald in a few days and stops any scabing, also one little tub lasts forever!
so once you have dabbed the tattoo clean with a warm water, slowly and carefuly put some tattoo goo on it, dont add too much because you dont want to block the poures of your skin, you need to let it breathe while its healing, a lot of recommended creams for tattoo aftercare clog poures and can trap sweat in and cause infections.... vaseline is a good example of this! never use vaseline for tattoo aftercare. yes, its used in the tattooing process but dont use it afterwards!
also try and avoid tight clothing over a new tattoo as you want to try and avoid anything rubbing on it for a day or two atleast.
other than that, just keep them clean and avoid soaking a new tattoo for the first week or so.
keep applying light coats of tattoo goo (or your chosen aftercare product) being carefull not to let it build up, try and wash the old stuff off before adding more... to keep it clean and that. dont just smear loads on thinking the more the better.

also, to keep your tattoo looking as bright and sharp as the day it was done.. avoid sunburn! make sure you put sun cream or sunblock over your tattoo, the worst thing for your tattoo is UV rays from the sun, my tatts get coverd in suncream when its even mildly hot outside and there still nice and bright.

hope this hepls anyone looking to care for their new tattoo,

Rob.