Myth: A wagging tail means the dog it’s attached to is happy.
Truth: A wagging tail signifies excitement; this may not be happy excitement, though, so read the rest of the dog’s body language before approaching!
Like most body language — this is true for all animals, not only dogs — one gesture doesn’t necessarily have a specific significance. Taking just one body signal on its own can cause you to misinterpret what that dog is communicating.
To get a clear message from the dog, you have to look at the rest of his body. With his wagging tail, he’s telling you he’s excited… But you need to know more! Is his body rigid or loose? Is his stare hard or soft? The way the tail is wagging is also important: is it languid, at times moving the rest of the dog’s body, or tense, almost like a rattlesnake’s tail?
There are many common signals (ears pinned, growling, wagging tail…) that by themselves don’t give you enough information to glean what is being expressed.
If you’re interested in learning to read dog behaviour, there are many great books with pictures depicting each signal and gesture. Then, book in hand, head to your local dog park, and watch the interactions between dogs. It’s great practice, and you may be very surprised by what you learn!