To set up the intranet with the publishing portal template, you need to have Global Administrator privileges. If you don’t have the right privileges, ask your system administrator to do the following steps:
1. On the Microsoft Online Portal, click Manage below SharePoint Online.
2. Click Manage site collections at the Administration Center page to display the dashboard.
3. Click New under the Site Collections menu and select Private Site Collection.
5.Below Select a template, click the Publishing tab and select Publishing Portal.
6.Enter the time zone, the primary administrator’s name (you), the storage limit, and the resource usage quota .
Once the setup the intranet portal we need to do branding and for that we need a good design for the intranet templates, view here few design sample for the office365 and SharePoint