Most Helpful Guy
First off, a henna tattoo is usually a brown base (brown, orange, reddish-brown etc). If someone got a black one, they could be in serious trouble, since black contains some pretty funky chemicals that don't always play nice with human body parts. So if there's any bright colours, then it's probably not a henna.
Henna tattoos only last for two weeks to a month at best. That means it'll look like a new tat. Simply ask where the person got it done. If they hesitate at all, they're full of sh*t and it's a henna. I currently have three tattoos, one dating back fifteen years, and I know exactly where I got each one, and can still name the artist of each. If it is a real one, they'll need to put some kind of antiseptic on it, so they'll be carrying the tube around with them.
Also, it'll look puffy and pink. If it looks fresh but with no sign of healing (as a tattoo is a wound, as far as your immune system is concerned), I'd call shenanigans. The other way to tell this is to give them a light punch on the tat. If their eyes don't tear up like a five year old with a scraped knee, it's a fugazi.
Depending on the time of year, what they wear can also give it away. Usually, tats are tender for a little while, so they'll wear loose clothing around the ink. If it's summer and they're smart, they'll be wearing something that covers the ink, as it can fade pretty badly in sunlight during the first little while. So if they have ink on their arms and don't have long sleeves or a bottle of sunblock nearby, they're either idiots or sporting a henna.
I'm sure that artists have many more ways to tell, but those are some of the ones I know of.