Concentrate on what the speaker is saying. This is mainly a mental action — rather than just “hearing” what is being said, you want to get in the habit of thinking about what the speaker is saying as they say it. This sort of concentration can be mentally fatiguing at first, but it gets easier with practice. Show that you are listening. This is mainly a collection of physical actions. Look at the speaker to show your attention. Nod when you understand what they’re saying. Say “uh huh” occasionally to show your agreement. Ask relevant questions.
Once you feel able to carry on a conversation with friends and family members, you can start going to places designed for meeting others: bars, clubs, large-group events (like parties or large-scale meetups), etc. All you have to do to start to start a conversation with a stranger is to say, “Hi, my name’s [x]! What’s yours?” You can also start with a talking point, like, “Wow, that’s a cool shirt! Where did you get it?” or “Oh cool, you like [band/show/book/something visible on this person’s clothing], too?”
If you ask someone whether they’re interested in something on their clothing and get an answer like, “No, it was a gift” or “It just looked cool,” you’re not out of luck. Try explaining how you know about the thing on their clothes and why you like it.
Try to pay attention to the dynamics of multi-person conversations. Notice when speakers change: usually, this is during a pause or after someone has finished a sentence, thought, or argument. You can often detect when someone’s ready to let others talk via tone. Listen for a note of finality at the ends of sentences, then pay attention to whether or not someone else chimes in.
If you feel that the conversation went well, this is your chance to set things up for another conversation with the person. Try saying something to the effect of, “Hey, I have to go, but I’d love to keep chatting later. What’s your number?”
Once you make some new friends, paying attention during conversations is still important. Focus on the skills you’re learning. Everything from recognizing speech patterns and mannerisms to picking up on conversation flow to commenting on important topics that come up can help you maintain your friendly connections as well as give you more experience.
Be ready — once you start, there’s a good chance your partner will ask you a few pleasantries about how you are doing.
If things do get awkward, remember that you can always simply leave!