With Office 365 P Professional and Small Business (P) plans you are required to switch the name server (NS) records to point to Office 365 hosted name servers. Office 365 Enterprise (E) plans do not require this.
Once the domain has been added to the P Plan Office 365 will automatically create all of the other DNS records (MX, TXT, SPF, etc) needed to run Exchange Online and Lync Online in the domain.
Once the domain has been verified in Office 365 you can create custom A and CNAME records using the Office 365 DNS management features. If you want to hosted email and instant messaging with Office 365 but host a web site with a third party you can accomplish this with Office 365 domain management.
Office 365 P plans only currently support creating custom A and CNAME records. You cannot create SRV, TXT, etc records with Office 365 DNS management tools at this time.
A good reference and how to video can be found at:
Domain help (E plans) – http://onlinehelp.microsoft.com/en-us/office365-enterprises/ff637610.aspx
Domain help (P plans) – http://onlinehelp.microsoft.com/en-us/office365-smallbusinesses/gg593305.aspx