Depth is better than breadth. The most interesting conversation in the room is the one you're having right in front of you. The Prophet (s) would make people feel seen and important. When meeting someone new, figure out what makes them tick. Find what their priorities are; don't just wonder how they can serve your interests.
Greet people you know and people you don't. Notice who is left out in the conversation and include them. One of the signs of the Day of Judgement is that people will only greet whom they know.
Be respectful of people's time. If someone needs to leave, let them leave. If someone looks uninterested in talking to you, give them a way out. Have a rich conversation with someone, but err on the side of making it too short rather than too long.
Try to remember people you met. It helps if you have a conversation with them to have a mental model. You don't need to exchange contact information with everyone you meet, but if they offer, you should save their contact. Shortly after, send them a message saying who you are and that it was nice meeting them.
When someone of the opposite gender wants to shake your hand, put right hand over your heart and say "It's such a pleasure to meet you," while maintaining eye contact. Try to continue the conversation until they slowly retract their hand. Don't draw attention to their hand. Remember, they are probably embarrassed, so the worst thing you can do is create an awkward silence where you're both looking at their hand.