Contact Custom Groups
Custom Groups are the most basic kind of contact group. This is the kind of group you will create if you click the "New Group" icon in the upper right hand side of the Groups page. Doing so will create an empty group. From there, you can search for contacts to add, or you can go to your contact list and add them to your group from there.
Custom groups are great to use as task-based lists, as you can add and remove contacts as you make your way through the collection. They are also useful for when you want to capture a subset of contacts who meet your criteria at a given time only - for example, maybe you offered some kind of incentive only to contacts who purchased a unit prior to the current date. You want to identify these contacts, but wouldn't want any future purchasers to be included in this group, so you would create a custom group.
The fastest way to create this example would be to go to the Contact Search page. Perhaps you've chosen to give your contacts a "Purchaser" rating when they complete the sale. Select that rating from the Rating dropdown and click the Search button. The page will reload with the results of your search. In the top right, there are two buttons - "Add to Custom Group" is the option you want to select.