I remember sweating bullets before emailing my professor for a recommendation letter. It felt super awkward, but I found a way to make it less stressful. I started by reminding them of the class I took, shared why I was applying for this opportunity, and included the deadline for submission.
What really eased the tension was attaching a short brag sheet that highlighted my accomplishments and skills relevant to the position. Also, I clearly stated that I understood if they were too busy and could say no without feeling guilty.
Trust me, this approach took a load off my shoulders!