I've become pretty savvy at meeting people and creating connections with others.
I wouldn't call what I'm about to say 'secrets' but I think this skill prevents a lot of people from making friends, getting close to others, maintaining friendships, and ultimately being happy.
The currency in my book is not the amount of money I have in my bank account but it's my self-worth plus the worth of the relationships I have.
Tip #1: There is no wrong way to introduce someone unless you don't. I fall trap to this sometimes. It can be really ungraceful; I can forget their names, but I need to introduce my friends with each other, so they may do the same. Often, my leadership sets the ball in motion. Set the example.
Tip #2: If I am not introduced, but my friend is talking to another friend, I will interject when polite and say, Hello I'm Charlene, I'm ____'s friend, nice to meet you. This does not need to be said with sarcasm, to make my friend feel bad, but it just needs to be done genuinely. I don't need to hijack the conversation; I just need to prevent myself from being an onlooker for eons.
Tip #3: In a situation where I don't know anyone, there is always the possibility of serendipity. Look friendly. Smile. This is so much easier said than done, and I used to have a huge issue with this. Everyone's face can wear a smile, and if it's been a while since it's been worn, it will feel funny. The more you do it, the more it fits, and the more you want to wear it. Ta-Da! People will gravitate towards you.
Tip #4: I always advocate being proactive despite the above 3 tips. If you genuinely have a comment to say in an elevator, or next to others in line, then by all means say it. The best thing that can happen is a flourishing friendship that happened due to a chance encounter in which a party said something. This doesn't mean say something in EVERY situation. That could be detrimental. The key is, when you have that feeling in your bones that you want to say something - you won't be offput by a lack of practice.
Tip #5: Talk to people as if they are already your friends. The key is to never overdo it. Feel your intuition. Overdoing it is as detrimental as not talking to someone at all. Obviously, if they do not reciprocate in kind, keep it cordial, and hope that a future encounter allows for more trust.
Tip #6: Create situational comments, ask questions, be genuinely curious about a person. If there's a common thread, exploit the hell out of it. (e.g. football game - obviously ask them about how they like UH, what their major is, how long they've been going to school here, what's their favorite place in Houston, etc. OR a birthday party - ask them how they know the host, ask what they got for the host as a present and compare gifts, tell them a funny story about the host)
Seriously. Making friends and keeping them in any arena - the book store, school, work, old friends, friends of friends, etc - is a HUGE skill everyone needs to know.
I love people. Making friends is the most fun job in the world.