What the achievement asks
Dance with another player on the dance floor at Norwington Estate. Five points.
It needs a second person, and it needs the right dance floor. Those are the only two difficulties.
The right floor
There is a second dance floor behind the mansion, at the top of the hill. It looks exactly like the one you want and the achievement does not fire there. If two of you have danced and nothing happened, this is why.
The dance
Both of you target each other and use the emote:
/danceThe other player can be from the opposite faction, which removes most of the difficulty of finding someone.
Only one of you needs to type it for both to get the credit.
For Horde players
Norwington Estate is deep in Alliance country and the guards are a real problem. The closest flight points are Wolf's Den in Tiragarde Sound and Mudfisher Cove in Drustvar.
If neither is unlocked yet, go west from the main Horde hub near Bridgeport, then swim north to the far shore.
Alone
It can be done with two of your own characters, which is worth knowing if nobody comes past.
Bring both to the floor, on the same War Mode setting so they share a shard. Start /dance on the first, then quit the game abruptly: the character stays in the world for a little under a minute. Log in on the second, target the first, and dance.
If they land on different shards, putting them in a group through the group finder first pulls them together.