TL;DR
Tail height tells you confidence. Tail speed tells you arousal. A high, fast, stiff wag is not a friendly wag — it's an alert one. Read the tail together with the ears and mouth, never on its own.
Height: how confident is the dog?
A neutral tail — held at the same level as the spine — is a relaxed dog. A tail carried high above the back is a dog that feels big and in charge of the moment. A tail tucked between the legs is a dog trying to disappear.
Breed matters here. A husky's neutral is higher than a greyhound's. Learn your dog's baseline first, then read from there.
Speed: how aroused is the dog?
A slow, sweeping wag is a relaxed hello. A fast, whole-body wag is an excited hello. A fast, stiff wag at the tip only — while the base of the tail barely moves — is a dog telling you to back off. All three are 'wags'. Only one is friendly.
Never read the tail alone
The tail is one signal. Combine it with the ears (forward and soft = interested; pinned back = worried), the mouth (loose and open = relaxed; closed and tight = tense), and the body weight (leaning in vs leaning away). A dog with a wagging tail, pinned ears, and a closed mouth is not a happy dog.