Firstly, this feature is fairly well documented. You should have received an email explaining the process when your account was initially provisioned. Here are a few pages that should help you:
In short, there are four options available for SAP:
You select a new domain to represent your brand, example: mycompany-email.com. Salesforce will purchase the domain and handle the entire configuration. There are no technical tasks required from your company. This is the easiest and quickest option.
You purchase a domain or use an unused domain you own, example: mycompany.net. This option requires the domain administrator at your company to delegate the domain to Salesforce by adding four nameserver (NS) records to the DNS for the domain.
You delegate a subdomain to our nameservers, example: email.mycompany.com. This option requires the domain administrator at your company to create the subdomain and delegate it to us by adding four nameserver (NS) records to the DNS and point them to our nameservers.
You host all the DNS records of a domain or subdomain of your choice.
These options are explained in this quickstart guide.
It sounds like you need option 2. You will need to refer to the Subdomain Delegation Guide, where you take your chosen subdomain and delegate it to the following servers:
Once delegation is complete, you should complete the SAP form at http://senderauth.herokuapp.com so Salesforce can configure your SAP.