The information in such forms goes to any email address that you specify in the code.
So you could either use your current personal email address, or you create a new one on Godaddy's that pertains to the domain of your pages.
Is it a shared hosting contract that you are on?
In this case, it's very simple.: You need to create email addresses on that domain you have with Godaddy's. Consider addresses like:
[email protected],
[email protected], or similar.
You can either only create them and let them forward mail to your present email address. Or you create corresponding mailboxes as well, then let the mail be delivered to those mailboxes, and you either point your email client application to the mailbox so it goes and retrieves incoming mail from there, or you simply use their webmailer to look for new mail.
The exact Howtos should be available inside your hosting panel.
Or do you actually have rented a dedicated or virtual server?
In that case you will have to either turn this server into a mailserver first (which is advanced stuff), or you simply let the contact forms send mail to your current personal email address.
Having a personal dedicated server for yourself just to haost some web pages would be massive overkill, though. In this case, consider downgrading your hosting contract.
