These three question words are often confused. Note particularly the following common structures.

How are you? (NOT Why are you?)
How do you do? (NOT Why do you do?)
What do you call this? (NOT How do you call this?)
What did you say? (NOT How did you say?)
Why should I like that? (NOT How should I like that?)

Both what about and how about can be used to make suggestions.

What about going for a long drive? OR How about going for a long drive?
She is a beautiful girl. What about / how about her character?

Note that what about…? can be used to remind people of things they might have forgotten.

What about the $50 I lent you? When are you going to give it back?
What about the cats? Who will feed them when you are away?

Both what and how can be used in exclamations. Note that what is used before noun phrases. How is used before adjectives (without nouns), adverbs and verb phrases.

What a pleasant surprise! (NOT How a pleasant surprise!)
What a splendid idea!
How wonderful! (NOT What wonderful!)
How you’ve grown! (NOT What you’ve grown!)

Other expressions beginning with how

A large number of interrogative expressions begin with how. Examples are: how much, how many, how far, how often, how old etc.

How much does it weigh?
How old are you?
How many people were present?
How far is the beach?