In central admin go to Manage Content Databases [
http://CentralAdminURL/_admin/CNTDBADM.aspx] and select your Web Application. Click "Add a content database" and fill in the form.
When done, you can move sites from one ContentDB to another by using the following PowerShell script
Move-SPSite http://servername/sites/sitename -DestinationDatabase NewContentDB
See Move-SPSite for more info.
For the record, SharePoint self-balance new sites to try to keep the number of Site Collection equal (by number) when new are created. That means a new ContenDB will get all new Site Collections until the numbers are equal with other Content Databases on the same Web Application.