After you have signed up for a BPOS trial you will be presented with a list of first steps. These first steps range from adding and verifying a new domain name, creation of a user account to creation of a SharePoint site collection.  Adding a domain name (yourdomain.com) to the service will allow you to send and receive e-mail on something other than the e-mail-admin@companyname.microsoftonline.com generic domain that is created when you first sign up for the service or a trial. 

The high level steps for adding, verifying and enabling inbound messaing on a custom domain are:

1. Adding the domain.
2. Creating a cname record for example.domain.com pointing to red001.mail.microsoftonline.com where the example part is supplied by Microsoft.
3. Waiting 15 or more minutes for this cname record to become available and then clicking verify.
4. Setting Exchange Online to be authoritative for the domain you have just added; setting the domain to the default domain for your services (username@domain.com where this is both the primary e-mail address and credential for the user).
5. Enabling inbound messaing on the domain.
6. Creating an MX record for your domain pointing to Microsoft's perimeter-based anti-virus / anti-spam system.
7. Waiting for these MX records to propogate.

Check out this screencast on how to go through this process.