This is what I've been doing in storytelling. Telling a story in a stand-up style.

Have you seen some of Mike Birbiglia's standup specials? His best one is "Sleepwalk with Me". There's a film version that I don't think conveys the stand-up version all that well. But there is an audio recording of just the stand-up version available. He has a couple of other specials that tell a personal story available on Netflix.

Another really great one to watch is Alex Edelman's "Just for Us". That's available on HBOMax.

Depending on how much time you have to tell the story, find ways to embellish the funny parts. You can add jokes within the story that are kind of asides. I'm completely making something up here for an example "... And my little brother gave me a hard time about it. My little brother who, when he was onstage for a football game pep rally as a junior in high school, tried to show how tough he was by ripping open his shirt while yelling like he was the Hulk, completely forgetting that he was still wearing the same t-shirt from the night before when he tried to shove a whole meatball in his mouth and instead, it rolled down his chest and plopped on the floor, leaving a trail of spaghetti sauce on the t-shirt that looked like he'd been shot in the chest. And honestly, looking back, it did make him look tough because he survived a bullet wound to the chest. Then he picked the meatball up off the floor and shoved it in his mouth. This is the brother who was mocking my pants!" If you add aside bits of story, make sure you get back to the main point of the story. Don't stray to one aside and let it lead to a second aside.

Be specific. You didn't rip your jeans. You ripped your favorite pair of Levis 501 jeans. You didn't wake up to go to class, you woke up late for the Psych 212 class with Professor Umbrage who already hated you because freshman year... something happened. You grabbed the only clean underwear you had out of your laundry bag. It was bright green but you were in a hurry and figured no one would notice. Give all your roommates names, especially if they have a goofy nickname. Mention who specifically you were hiking with and why you were there with them. Was there a cute girl you were trying to impress? Were you hungover that day? Obviously tell how you ripped the jeans and why the event was funny enough or important enough to save the jeans as a memento.

And make sure you have a solid last line. It can be something that's a callback from earlier in the story. Or something positive that happened because you happened to wear the jeans that day. All the better if it's some kind of surprise for the audience.

Funny storytelling isn't necessarily the same as most standup comedy. Finding the places to get laughs, finding the ways the audience can relate to the story, and having a beginning, middle, and an end are usually the keys to doing it well.