The acronym is DEAR, which stands for Describe (the situation), Express (emotions), Ask, Reinforce (why should they do it). Really simple.
Describe: Gordon, I’m not a bit surprised that you thought the paper was rubbish. To be honest, I had the exact same feeling when I was writing it. I felt like I was rambling on and on.
Express: I’m always amazed when I read your papers because they’re so incredibly clear and lucid. That’s actually one of the reasons I wanted to work with you and why I was so excited when you offered me a position last fall. The results of our research could be extremely important, and I know that if the paper were well-written, it might make a tremendous impact.
Ask: The paper may be beyond repair, but I’m wondering if you might have any suggestions about how I could make it better.
Reinforce: I want to learn as much from you as I possibly can.
You can structure basically any "ask" this way, even a really brief one. I've found it really useful, especially when planning out in advance how I'm going to ask someone for something. Protip: A good DEAR can be 50-70% reinforce :-) In fact if I had made this hypothetical-paper-editing ask I would have moved the last sentence of the Express to the Reinforce to introduce the question earlier and backload the importance of the paper after asking for help improving it.