It really depends on a lot of things.
You are booking a flight from point A to point B via Delta. If changes need to be made in advanced, you will hear from Delta. You may be moved to a different airline altogether. If you need to make changes, you deal with Delta
If you don't like the changes you receive in an email, you contact Delta.
If the flight is canceled the day of your flight, you will probably deal with the operating airline for an alternative although that airline could tell you to contact Delta.
For compensation, you have to wait to see which airline contacts you. Airlines are required by law to contact passengers that may be due compensation under EC261 and they have to tell you how to apply for it.
I recently had a Finnair flight canceled. Finnair rerouted me with a one stop itinerary rather than a nonstop. (There were no other nonstops.) The first flight was on Finnair, the second flight on British Airways. I was able to check in for both flights on the Finnair website.
Finnair contacted me a day or two later telling me what compensation I was permitted and gave me a choice of voucher or cash. I received the "cash" as a direct bank deposit within a week.
So, my advice is deal with the people making the changes and don't worry about EC261 until you need it.