If someone shares a story and you have a similar story to share, that is usually a good entry point. Don’t do this everytime someone shares a story - the goal should be to make them feel like you heard them and can relate in some way rather than to actually share.

Another good way to show that you are actively participating in the conversation is to ask follow-up questions. If they are talking about a recent vacation, for example, you can ask them what made them choose the destination they ended up at. Most of the time you don’t actually care about this information, but that’s the price you pay to engage. If you’re clever about it, however, you can sometimes use these follow-up questions to steer the conversation toward a topic you’re actually interested in.

Note that neurotypicals will call you manipulative if they catch you steering things toward your special interests too often. They’re right, I guess, but they all do it all the time, too - they just don’t notice because they don’t have to put conscious effort into it. If people resist your topic, just try your best to set it aside for another time.

I would counter the last argument with taking group convos like entering a mini game where everybody is listening and also wants to add something, but only if they feel it’s worth is above a certain threshold. So there’s a cadence to a group conversation endemic to the combination of people in it, and entering a thought at the wrong time adds a kind of debuff to that thought making timing and waiting for somebody to finish their thought very important.

Secondly, the threshold is context dependent depending on the current topic being discussed. I find that it’s always nice to figure out combinations of words that enable other people to be able to speak more freely effectively lowering the threshold. Here is where you can talk about yourself if you’d like, although you don’t have to, but always try to make your point something that opens up conversation for the other person. For instance, if somebody is talking about something they did over the weekend you can ask about if they do that thing a lot, or you can add something similar you’ve done and what you thought was cool about it and if there’s anything the other person enjoyed about it etc.

Conversations are a balance of give and take, and really dialectical in that sense. It’s not an antagonistic contradiction of what you want to talk about and what other people want to talk about but rather finding the ground where you are both enjoying the conversation, which also sometimes means just listening to what other people have to say.

This is a difficult problem for basically anyone, so it helps to remember that nearly everyone struggles with this in unfamiliar environments. Even people who don’t struggle with this problem probably had to develop the skill by just trying and failing. It takes practice.

A way to approach it, assuming that you’re in an environment where it’s expected that people will mingle, is to listen to conversations until you hear something that resonates with you. If there’s a moment to interject, say something positive in response. Just agree with what’s being said. People like being validated, and people will like you if you validate them. If you’re warmly received, ask a question that gives someone an excuse to elaborate or agree further. Just be nice, smile, and tell people that you like what they’re saying, then just sit back and listen. If you feel like you’re not getting good feedback, just exit and go talk to someone else. The idea is to test the waters, leave a positive impression, and don’t make anyone feel like you’re butting in on their conversation or overstaying your welcome.

The trick is to have fun doing it. If you look like you’re having fun and helping other people enjoy themselves, people will respond positively and want to include you in the conversation. Worst case scenario, they won’t hold it against you for being nice. Practice it and do what feels good, and stop the moment you get overwhelmed or feel uncomfortable.

Lastly, remember that no one will hold it against you for politely trying to make conversation and stepping away if you get the sense that they don’t want to chat with you. What people dislike is when others are negative, argumentative, or linger in a conversation when its clear there isn’t any reciprocation. Taking little moments to make comments or ask questions and then moving on is a good way to get used to entering conversations naturally. If someone does take what you’re saying the wrong way, simply apologize, say you didn’t mean anything by it, and move on. Do it often enough and you’ll get a sense for when people want to engage further. It takes practice, but it doesn’t have to be a big deal.