Attributes and their groups allow your customer to filter products in a category based on commonalities about your products. For example, if your store sells TVs, your customers can use attributes to filter by screen size - a common element seen on many web sites. 

First, you will need to create an attribute group to contain all of the grouped attributes. In the attached screenshot, I created an attribute for Screen Size. This can be done by clicking New in the Top right.

Once the group is added and saved, you can begin adding attributes in the bottom section. First select the attribute group name then add a new attribute by Selecting New Attribute

Once you have added all of the needed attributes, save all of your changes and open your product to edit. Then, move to the attribute tab. This will display the attributes assigned to the product. Click the New Button in the Top Right to add a new attribute. Select the group and then the specific attribute that applies to that product. The value field is arbitrary and is not used for sorting, so it is not required to fill it out.

Save all of your changes to the product and you are done adding the attribute to your product!