You can add a new group from the Magento admin area->Customers->Customer Groups->Add New Customer Group.

Once a customer is registered you can change his/her group from the Magento admin area->Customers->Manage Customers. Click on the Edit link besides the customer and change its group from the Account Information->Customer Group. Click on the Save Customer button.

Set the discount from the Magento admin area->Promotions->Catalog Price Rules->Add New Rule.

In the Customer Groups select the customers' groups for which the promotion is valid. Enter the other details, set the rule's actions and conditions.  At the end click on the Save Rule button.