SharePoint 2010 provides different permission groups by default like Members, Owners, Visitors, Viewers etc. But all SharePoint Administrators can be able to add new SharePoint security groups to SharePoint 2010 site collection. To create a new group. go to Site Actions -> Site Permissions as shown in the figure below. 
In this page you can be able to see all the default groups also. And from the ribbon click on Create Group as shown in the figure below to create a group.
This will open the Create New SharePoint Group page. And in this page, Give a name for the group, Description for the group and also the Group owner and the membership of the group like who can view and edit the group as shown in the figure below.
And also in the Membership request section you can do the settings and Give permission to site is an important section since we are giving permissions to the site. You can choose from the list of permissions like Full Control, Design, Contribute, Read, View only etc. as shown in the figure below, then click on create and our new group will create.
Then you can add users to that group by following this: