...has/have a wonderful day.

It should be "have"--everybody is an indefinite pronoun, of that class of indefinite pronouns which are treated as singular. It gets tricky here, though. In your sentence, you are addressing everybody just as you would address one or more individuals. That is because your sentence is an injunction--a sentence which tells someone to do something, or to refrain from doing something. "You sit down. No, don't sit there, sit by the door."

There is no distinction in modern English between the second person singular and the second person plural, and both use the second person plural forms of verbs. So, even though everybody is a singular, indefinite pronoun, in an injunction it is being used just as a second person pronoun would be used. Therefore, you would use have, which is the verb form for the second person, singular or plural.

In declaratory or interrogative sentences, everybody is treated as a singular pronoun--"Is everybody happy?" "Yes, Bob, everybody is happy, now can we get on with it?" In both of those cases, everybody takes the third person singular form of the verb.

I hope this is clear to you--if not, i'll try to do a better job of explaining it.

Thanks, Setanta, for the detailed explanation. It is clear.

You're welcome.