I remember the first time I needed to ask a professor for a recommendation letter—it was super nerve-wracking! What helped me was crafting a straightforward email. I included a brief reminder of the classes I took with them, explained why I was applying, mentioned the deadline, and attached a one-page brag sheet.
Also, I made sure to give them an easy out if they were too busy—I said something like, 'I completely understand if you can't help with this.' That really took the pressure off!