As far as I can understand, when you create a game and select the "Collected by itch.io" option, itch.io generates tax forms for you. What happens then? Do they send that tax form to me? Do I need to send them by mail to someone or email the form to someone? And do I have to pay anything? What exactly do I have to do?

The VAT is collected and reported directly by Itch, as Itch is listed as the seller.

Once a year, the company that uses Itch for taxes sends you an email with the corresponding form that reports the withholdings from your account.

You must use this form to file your tax return, but since this depends on the laws of each country, it's best to consult with a tax attorney.