If you are using the UPS shipping mod only, then you won't be able to offer "free ground shipping" (well, you could, but it wouldn't show in the cart, and the customer would have to pay for it ... not what you want).
So, to use the UPS mod and offer Free shipping, you need to have at least two modules installed.
- UPS
- The Free shipper Module.
However, that too may not get you what you want. So, what I did was installed the UPS module, Installed the Free Shipping Module, and then CLONED the "Free Shipping" module altering it to work with UPS.
I only did that because I wanted to offer free ups ground shipping over a certain dollar amount. It worked. (that was for an older install .. the newest version has this concept "built in").
Now, the "easy" way would be to install the UPS module via the Admin, Install the "Free Shipping" module via the Admin, and then change the "language" of the free shipping module to read "Free UPS Ground Shipping" (instead of the default "FREE SHIPPING" text that is there).