Please help.
Is it correct if we ask, "What did you do today?", and what is the difference between "What did you do today and What do you do today?"

Thanks for your help.

What did you do today?
Answer: I went to the zoo.

What do you do today?
Answer: I am a plumber.

Did is the perfect aspect of the verb, whereas do is simple aspect.

GM is correct, but "What do you do today?" could also be a question about the day's scheduled activities.

A: "Have you seen the schedule?"
B: "Yes I have it right here."
A: "Please look at it. What do you do today?"
B: "Let me see. Ah, it says here I see that I have a meeting at three o'clock this afternoon."

I find 'What do you do today?' a little odd in that example. I agree it's totally understandable, but it's in the wrong aspect methinks.

The present simple tense is commonly used when talking about future events when discussing schedules.

Ex:
Your train leaves at six AM tomorrow morning.
Fine. When does it arrive?
It arrives at two in the afternoon.
Ok, what do I do when I get there?

Ex:
Check the schedule. What do you do today after the meeting?
Hmmm, let me see... I have a presentation in the conference room.

This is not just something I have noticed. See Betty Azar's Understanding and Using English Grammar, Chapter 4, on Future Time, for example.