As far as starting relationships, it's not as different for women and men as it used to be. For instance, my wife asked me out. Similar to Callie above, she said that she didn't want to wait around guessing, so she just took the plunge. If it didn't work out, she said she just planned to move on. That was not only very refreshing and impressive, it worked out very well for both of us.
When I was dating, I tried to be friends first. It's possible, and very likely, to be attracted to people that you have absolutely nothing in common with. You won't know this until you spend some time with them. I tried to have a few dates that weren't really "dates" first to see if I wanted to continue. It created far less pressure for both people. Plus, if she said no to a casual date then it was pretty likely that she didn't want to date me at all.
As for trying to get into her line of sight or waiting for her to notice you... you could be waiting a very long time. And you could end up looking strange or creepy. If you're interested, just try to start things slowly. Find some innocent reason to talk to her. Also, don't rely too much on physical attraction, because you may end up liking her looks but not her personality. Attractiveness never makes up for a bad personality. Some people have to learn this the hard way.
But if you're interested, definitely do something. Talk to her. Ask her to lunch. Anything.