Sie haben sich für den kostenlosen E-Mail-Newsletter "Naturmedizin aktuell" angemeldet. Damit wir mit der kostenlosen Belieferung beginnen können, bitten wir Sie nun noch, Ihren Auftrag zu bestätigen.
'Sie' is used as the polite form of (singular) you here. I saw you translated it this way in the last sentence, but the first one says 'they' instead
My suggestion:
You have registered for the free electronic newsletter "Naturmedizin aktuell" (or your translation which is fine).
In order for us to start sending it, free, we ask you to confirm your order.
What do you think?
I am not completely happy with 'start sending it', but I think 'supply' is not the best word here either. Once I have started a poll we can see if anyone else has a suggestion
Yes, that's a good suggestion! I have edited. I have also removed 'free' because I think the first sentence makes it clear already that the newsletter will be free. Let me know if you don't agree!