It serves no purpose to try and connect by telling others how great you are. Self-promotion often comes across as arrogance and is a sure-fire way to fail. Trying to impress others is not the best tactic for networking. Why not?
Well, to start with. When you adjust your behaviour to cater to what you think others want to hear you become anxious, even you are unaware of it. Being someone you are not authentically is stressful and this anxiety will come across in how you project yourself. Even if you are the most authentic person you will appear inauthentic and your networking attempts will backfire.
So what do you do? Especially if you are not a very confident or extroverted individual. To start off with, just be yourself. You know better than anyone what your strengths are and you will know what to talk about that will show these characteristics. Being at ease with yourself, will make others feel at ease with you.
When in conversation, ask questions you are genuinely curious to know the answers to. And if you do not know much about the topic being discussed, be genuine enough to admit this and ask for more information. This will encourage others to share more openly with you. Do not be afraid to admit that you do not know everything about everything.
And most importantly, be sure to engage with those you are speaking to by making eye contact.