The rule is you must approach and initiate a conversation within 3 seconds or else she will perceive you as a stranger.
Even if you really cannot think of anything to initiate a conversation with a girl, whatever you do, don't break the 3s rule! Act in 3 seconds nevertheless, even if you have no idea, how to continue. If you act in 3 seconds, she will notice it, no matter where she just popped in from or where you popped in from or how you happened to pass each other by in a given geographical location. She will see the spontaneity in your approach and it will work in your favour. If however you wait and hesitate and then decide to approach, you are in a decidedly weaker situation.
If you just arrived and accessed her in 3 seconds, she will know it was spontaneous because she noticed you arrive whether she wanted to or not - you were a change in a static environment. Or if she just arrived and you accessed her in 3 seconds, she will recognise the spontaneity of it again, because you couldn't have accessed her before - she simply had not yet arrived. If however you just pop out of nowhere - she didn't see you arrive neither did she just arrive and the only change in a static environment was you accessing her - you just might set off her stalker alarm. Who knows, how long you've been following her or watching her in secret or gobbling her up with your eyes. Spooky! Argh, get away you freak! So the only way to avoid a situation like that is to use the 3s rule. Besides not setting off any alarms of her because of the obvious spontaneity of your approach, you are also doing yourself a favour. In three seconds, you have no time to become sweaty, trembling, stuttering - to acquire all the sure-fire signs of an AFC lacking any confidence, substance or consequence, a failure with women and life in general, a complete repellent of beautiful girls. So even if you start sweating, stuttering and trembling while talking to you, you weren't that way when you initiated contact - you just didn't have the time for that. And it's the first impression that counts. And if that first impression of you was that of a confident and spontaneous man, her feelings for you were positive from the star, which in turns greatly the diminishes the chances of you turning into a plateful of jelly while having a conversation with her.
The 3 seconds rule of course is not an absolute - you may simply not have noticed her, while not specifically being tied up with something that might have stopped you from approaching her, or while still noticing her, you might have been busy with something (or somebody:). The three seconds start counting from the moment you have spotted her AND are free to approach. But when these two conditions are met, you really don't have the time to ponder, whether or not SHE noticed that you didn't approach her because you were either too busy or simply oblivious - the clock is ticking, so move it!
The worst part of not using the 3s rule is when the girl sees you hesitating. Don't stare at her for 10 minutes approach. That's creepy. Don't walk around her pretending to be busy looking for something and then suddenly approach. You'll look fake and weak. Don't stand beside her wondering to yourself waht to say and then approach. You're approach will look canned and no spontanity.
Do pick out something about her to comment on. It could be a book, something they are wearing, questions about something that they MAY (not necessarily DO) have knowledge on, something we have in common, whatever.
All rules have exceptions. The 3 second rule is not set in stone. It is simnply nice guideline to follow. You do not need to time yourself. The purpose behind the 3 second rule is simply to approach when she is notices you. This gives you momentum while prevent her from creating a protective shield to stay away from strangers.