The standard way to assign global groups to specific products is selecting the ‘By product’ rule in the global edit screen, then assigning products. You can see how to set that up here.
However, you might wish to assign some global groups to a product directly from the product edit screen. You can do that by selecting your global group(s) in the ‘Assign global groups’ field on the ‘Product Add-Ons’ tab.
Now, all the fields in your selected global groups will be applied to this specific product.