You can add a new customer's group through the Magento administrative area -> Customers -> Customer Groups -> Add New Customer Group.
You can set the discount for the newly created group through the Magento administrative area -> Promotions -> Catalog Price Rules -> Add New Rule. At the creation page using the Customer Groups fields you can select the customers’ groups for which the promotion will be valid. Enter the other details, set the rule’s actions and conditions. At the end click on the Save Rule button.
Once a customer is registered you can change his/her group through the Magento administrative area -> Customers -> Manage Customers. Click on the Edit link besides the customer and change its group through Account Information -> Customer Group. When you are ready click on the Save Customer button.