How does One Make New Friends?

I just read an article on HelloGiggles.com called 6 Signs You Need Better Friends.  Now don't get me wrong, I have a group of really great friends, whom I love dearly.  However, of that group of friends, one or two really stick out as matching quite a few of the requirements in this article.  I have friends who CONSTANTLY bail, or who try to one up whatever issue or problem I may be having with one of their own.  I'm sure we all do, and as my family and other friends sometimes point out, maybe it's time to move on from those friends.  However, how does one do that?  I think I've been spoiled because I've always been able to make friends relatively soon.  I don't know if it's me, or if I just like to know things about people, but I'm usually pretty good at making a good first impression.  In school years, it was easy.  You had something in common with people and for the most part you hung out around the same people, especially as you got deeper into your major or your extracurriculars.  As a full-fledged adult, who works in a very small office, it is really hard to make lasting friends.  Sadly, I can count on one hand the friends I have made as an adult.  And I don't know what it is.  Maybe life?

But let me give you an example*.  Say you go to a party, or a club meeting or a social hour, whatever.  You go someplace where other full-fledged adults are congregating.  You get a drink (because every awkward is seriously better with libations), and you mingle.  You may meet someone who you kind of hit it off with, but not really. Or you may meet someone that you totally click with (we're not talking romantically, just friendly).  You have the same tastes in books and movies, and she (or he) is even madly in love with the same off-beat celebrity you are!  This is kismet, this is fate.  Here is your new best friend!  So you exchange information, and you go on.  But then you don't hear from her.  You find her on Facebook, and you add her, and she accepts your friend request.  We're doing well so far.  Then you post on her wall about something that you talked about.  No reply.  Somewhere along the way between awesome convo at social gathering and now, the friend fire cooled, and what do you do now?  You don't really know this person, so you can't badger them like you would your friend you've known for years.  You'll come off as a weirdo, in a bad way.  So what do you do?  How do you take that great conversation in a social setting and turn it into a lasting friendship?

*Note, all examples are totally hypothetical.  I'm not cool enough to go out into social settings with other full-fledged adults.  In hindsight, maybe that's my issue.