What specific fitting do I need to connect a 1/4" copper refrigerator water tube to a 3/4" steel water line that's already in use?
I think kitchen sinks are 3/8" (but I can never remember). So you'll want a 3/8" female, 1/4" male, 3/8" male tee. You should be able to find one at the local big box, or hardware store.

Something like this




Shut off the water using the shutoff valve.
Remove the existing supply line.
Attach the tee where the supply line used to be.
Connect the sink supply to the 3/8" male outlet on the tee.
Connect the refrigerator supply to the 1/4" outlet on the tee.


NOTE: Use your preferred pipe dope method (tape or goop), however, since it's a brass fitting dope should not be required.