It works like this:
Create the attribute by clicking “Add New Attribute” under “Catalog > Attributes > Manage Attributes”
After you have created the attribute, go to “Catalog > Attributes > Manage Attribute Sets” and click on the “Default” set to open it. Your new attribute will be on the right side of the page under “Unassigned Attributes.” Drag and drop it into an attribute “Group” and click on “Save Attribute Set.” You can create a new group to hold it first, or use an existing one.
Now, when you go to “Catalog > Manage Products” and “Add a Product,” the new attribute will appear in whichever attribute group you assigned it to, which can be selected from the left hand navigation.
You can also set up multiple atttribute sets to use with different products. For example, if you sell t-shirts and books, you could set up t-shirts with size and color and books with author and publish date, etc.
I hope that helps.