Let's talk about introversion vs extroversion first to get a perspective. Odds are that you are introverted, not only because you are asking for advice, but I'm pretty sure most people are introverted. In my experience, at least 80%+ of people are introverted base (ie. they would rather not do the extroverted approach and begin the conversation, as opposed to real extroversion of thriving on it). My experience is based on retail (op shop), where I randomly meet a bunch of people, at least 40 a day. This is the important base: most people you are going to meet, are not going to start the conversation.
Why is this important? It is important because even if you are introverted, which you probably are, you are probably gonna have to do all the shit parts of starting a conversation: saying hello, starting the conversation, risking rejection and getting snobbed.
Now you know where you are starting from: you pretty much have to do everything, how do you actually do it? The answer is that it is really easy. This is the other reason why I guessed that you are introverted. If you were extroverted, you would have just talked about any nonsense, and bam you already have a good conversation going. That is the how, just talk literally about whatever.
To recap a bit more (not to go too heavily in depth), start by introducing yourself: "Hi, I'm prodigy2, I'm an avid redditor and I like puppies.", then gauge their reaction (If you already met, after remembering their name, ask them how they are). Depending on whether they are extroverted or introverted, either start listening, or start telling a story:
"Last night I got terrible sleep, my dog who is...(dramatic pause)... terrified of any loud sounds. So when the thunderstorm happened, she barged her way into my room. She ran into the tiny gap between my wall and the bed and started panting in a furious... like a panicked state. So I had to keep getting and petting and calming her until she fell asleep.
This was a story I told about a week ago, right as there was 4 introverted people who weren't very comfortable with each other, and thus was an awkward silence. While I tried to write it as verbatim as I can remember, it was probably much messier than that. You don't have to speak perfectly. That was enough to open the conversation and for them to start talking about their pets.
I just told you two stories, in 'good storytelling structure'. This is part of the "how do I...". Good storytelling structure has three parts: introduction/setting the scene, the conflict/content and the resolution. Missing any of these parts can cause alienation (no scene setup/'you should know since you were there'), boring (no conflict/content), or unsatisfying (no resolution). Go back and try to notice those parts in the stories, and try to include them when you tell yours. Practice crafting your own stories. Then eventually it will come naturally. This idea has much more depth but I'm too lazy to elaborate.
Good luck and get out there and practice.
PS: I am introverted too, and I am skeptical that the extroversion "you gain energy from being with people" is a real thing. If you met me you would think that I'm a confident extrovert but I'm not. Ask me in 5 years whether I think extroversion is a real thing or everyone is 'faking' it.