When I did it I approached authors I admired personally through their contact form, really politely. Plenty didn't respond and that was fine. But I ended up getting a few through, including Malinda Lo and Robin Hobb. Others were friends who were also authors.
When people approach me they have to be in a similar-ish genre, and ideally I'll know them at least a little through social media. I tell them what date I'll get back to them with a blurb. If I don't make that date, it means I didn't have the time, or I didn't feel comfortable for whatever reason.
My requests followed this sort of format:
Dear [author name],
I hope you don't mind me dropping you a line, but I was wondering if I could ask a favour.
[Bit about who my publisher is, when I signed, etc]
[short pitch:] Pantomime is a YA fantasy. It’s about a daughter of a noble family, Gene, who doesn’t fit into a life of tea parties, corsets, and crinoline. After discovering secrets about her past, she runs away and joins R.H. Ragona’s Circus of Magic as a boy named Micah Grey, but the past refuses to stay in the past. Micah/Gene was born both male and female, with neither gender fitting completely. I also have several other GLBTQ characters in my book.
[why I approached them specifically - read and liked their book, follow their blogs on X subject, etc]. I understand you have many calls on your time, but if you could fit reading Pantomime into your busy schedule, I would be so honoured.
I've included a few links before for more information if you're interested.
[links to press release and the product page]
Thanks for your time and consideration, and please let me know.
Kindest regards,
Laura Lam