My brother and future sister-in-law asked me to read Elizabeth Barrett Browning’s "How Do I Love Thee" for their wedding ceremony a few years ago. Afterwards, people complimented me and asked about my acting career. None. I’m an English teacher, former college poet, and professional writer who reads at science fiction conventions. So, lots of practice reading in public with a teacher voice which don’t need no stinkin' microphone.
For the wedding performance, I used a huge font and printed the poem on heavy-weight paper so I didn't need support for the paper since I didn’t have a podium, and the paper didn't make noise. Since it wasn't my work or my natural rhythm, I also listened to professional actors perform it online, then read it to myself enough to figure out where I needed to drop a word or change the rhythm slightly to fit my voice.
For my own work, I figure out how each character's voice sounds and remove all the dialogue tags like "said" which clunk when reading a story aloud. (If you want to see how a genius voice actor works, listen to Jim Dale's performance of the Harry Potter series. Incredible!)
I also pick one of my short stories of the right length rather than a book chapter or two because I'm performing, not slogging my books directly. Funny with a small cast is better than dark and violent for most groups, plus kids may be present. My favorite is "The Werewolf Whisperer" about a werewolf trapped in his wolf form in an animal shelter where he will be gassed or neutered. Neither is a good outcome. I've linked below if you want to snort your coffee through your nose at the ending. (You and your keyboard have been warned!)
Also, just relax. People come to these events to learn about you and your work, and most are friendly. The jerks can end up as a victim in your next work.
If you have extra time at the end, let the audience ask questions.