Learn Swedish: Hur mår du idag? - How are you feeling today?

The base verb here is må (to feel/be doing). It belongs to a group of short verbs that already end in a long vowel. To make them present tense, you just add an -r to the end, making it mår.

Can I translate 'How are you?' literally as 'Hur är du?'

No, in Swedish you cannot use är (are) to ask about someone's well-being. 'Hur är du?' would sound like you are asking 'What kind of person are you?'. You must use the verb mår to ask how someone is doing or feeling.

I've seen the word 'känner' for 'feeling'. Why use 'mår' here?

Mår is specifically used for your general health and well-being. Känner is used for physical sensations or specific emotions, like feeling cold or feeling sad.

Is 'idag' always written as one word?

You will see it written as both idag and i dag. Both are perfectly correct and mean 'today', but writing it as one word is very common in everyday Swedish.