First of all go to Settings > General Settings, in that go to Portal Access portion, in that select Allow external users to signup to enable sign up option in website.

After configuration, to create new account just go to Sign in and in that click on Don't have an account?

By clicking Don't have an account? link you will redirect to following screen. In that you have to fill details like Name, Email, Phone number and your company and click Send to make portal user request.

And you will get confirmation message on this, if your data are corrects.

When you send request then the system checks that:
1) using given name and email, is there any partner exists or not as a person if not, then create new and
2) Also check that based on given company name, is there any partner available as a company or not, if not then create new partner as a company

Actually when you send request then it goes to crm module in the form of lead and the sales team authenticate request based on filled information.

If user has submit twise request/more then one time and request is sended but not authenticated still then system gives alert message that "We will contact you shortly.."

If user has submit twise request/more then one time and request is sended and authenticated successfully then system gives alert message that "You are already member and login to continue..."

When system accept portal user request from helpdesk then they need to create user manualy and send confirmation mail and send credential to that user.

Based on Sign up request, system automatically create company and in that create user in contacts. In that the user is belongs to that company

You can see the coming request to crm module with title New Portal user request from here sales team authenticate that request and create user from this contact details and communicate using that email.