This is something DotNetNuke can do for you already without having any extra code written. 

You must first set up the system to allow this functionality:

First, log in as host and navigate to Host -> Host Settings.
On this page you will see a section called "Payment Settings", expand this section.
In the section there is a check box to allow an "Anonymous Demo Signup?"

When is this is checked you have enabled you site to allow users to come along and create a new website.

Remember to update the page and save the changes.

You will need to add this link to your signup page so to give people access to the DotNetNuke signup section:

http://[localhost/Dotnetnuke]/Host/Portals/tabid/17/ctl/Signup/mid/321/portalid/0/Default.aspx

Replace [localhost/Dotnetnuke] with your domain.

I hope this saves you some of your budget

I would consider a more functional add-on for this purpose. The built-in stuff is pretty limited. Onyaktech's Portal Sign-up module is  the one to look at.

Rob