I want to know how the Threefish cipher can be used to encrypt and decrypt. I tried to find out by searching the Internet but can't find a concrete answer. The only answers are theoretical in nature which is not usable to me.
As far as I know there isn't any Threefish-specific encryption standard specified. I actually asked Bruce Schneier back in the day (when I created my "SkeinFromSpec" implementation). Threefish is a tweakable block cipher with a large block size. I asked for instance if you should keep to the high amount of rounds (80 for Skein) and what mode I should use, but I never got a concrete answer. At that time the Skein team was of course mainly busy with the SHA-3 contest.
In principle you could use any mode of operation that is also available for normal block ciphers, as long as it allows for the larger block size. You are of course better off using an (authenticated) mode of operation for tweakable block ciphers. There are a few papers on that, but as you've indicated, they are usually theoretical in nature.
Things may have been different if Skein was the winner of the SHA-3 contest. There are a few proposed modes that use the Keccak sponge - the winner of the SHA-3 contest - which you could use, Keyak for instance.