Going up from the kitchen sink shutoff valve(s) toward the faucet is a 3/4" outside diameter hex nut and then 3/8" copper tubing to the faucet. The new faucet has compression fittings. How do I remove the old connection and prepare it for the new fittings?

Purchase a set of tub and shower wrenches.
Remove 3/8 supply tube from stop valve.
Slide proper size wrench up over the supply tube and unscrew mounting nut.
Note that one wrench will fit inside of another such that 3 or 4 of them stacked together will extend down below the sink so you can turn them with the included handle bar.Attachment 46410