I've been with my husband for 21 years (married for 18), but I can tell you about most relationships I knew about in the 1980s, when I was in high school and college and in the early 90s. My experience may be atypical though; especially to how it correlates to nowadays since no computers were involved.
Group dating was popular in the high school with hook-ups happening then, at parties or during group after-school activities (football games, drama, band, etc.). Every dance I went to in high school, I asked the guy to or we were already involved, so it was just assumed that we would go.
The only "date" I was ever asked on (where the guy called and asked specifically for me to go "out" with him on a date) I wasn't interested and so said 'no'. The experience probably jinxed me as I was never asked out in such a manner again. (I my opinion, if you've kissed someone -- really kissed them, not just a small peck -- in a casual setting prior to going out just the two of you, a form of relationship has been established and therefore any requests for dinner, movies, 'going out', doesn't count as being asked on a "date" per se, but as "dating". But maybe it's just my wacky way of seeing the world.)
When I lived in Germany during a year abroad, the only guy who expressed interest in me (we went out on a group date to the movies) made it clear through his actions (and then words) that he thought I was loose and would jump into bed with him just because I was an American, which I found insulting. Needless to say, he didn't get what he wanted and I didn't go out with him again. It just proves that every culture has their jerks, since he wasn't like most guys I met while I was there. He was the only one I kissed though.
In the small liberal arts college I went to, group dating again was the norm with hook-ups (not necessarily sex, usually just kissing) happening at parties and while 'hanging out'. Rarely, did guys ask a girl "out on a date" to a party or school event if they weren't already involved.
I met the man who would become my husband in college. I invited him and his friends to several joint activities I was doing with my friends. He did the same. We were involved in some of the same groups in college and were friends first. Group dating in this way is very vague (read: frustrating) because mostly it's just a group of friends hanging out. Until he kissed me, I wasn't sure that he liked me as I liked him.
I had a personal rule, where I might invite a guy out (really, it was the only way since they never seemed to ask me out), but I would never initiate the first kiss. Then I assumed we were in a relationship until I was proven otherwise (I mean, why else kiss me, right?) Maybe I was naive, but it seemed to work. So, according to your linked article, I must date like an Australian.
In my senor year of college, I asked my husband to marry me (by asking him if he could ever see himself married to me), but we were never formerly 'engaged'.
After college, he returned to his home country (because his school visas were expired) and I tried to get a job in an office rather than retail. After a year of missing him and hating dealing with the lack of career opportunities for a college graduate, I moved to his country and we got married. Again, I initiated this action (when I called, he thought I was calling to break up with him). I hated my life as it was and I figured misery loves company.
I don't think my 'dating' experience is typical for Americans, especially nowadays, but it's what I know.
My sister, on the other hand, has never had difficulty having men call her to ask her out. She has met men a numerous of places (including online dating), they'd exchange phone numbers, they'd call her (or arrange to meet), and they would go out on 'get to know you dates' as you see in television shows. Sometimes, they would continue dating; sometimes, she would never hear from them again. She's currently in a relationship with a man, I believe she met online.
I don't think there are any set "rules" for dating in America, since we are a mish-mash of a bunch of cultures; it's a matter of personal choice and which 'rules' you set for yourself, which could or could not be based on family values and/or cultural traditions.
