Give some detail.

a typical failure is as followed: I follow the 3 days waiting rule before texting and calling but every single time the girl sound like she is not interested at all and then it crashes and burns from there.

That's obviously part of the problem. Waiting three days to call a girl is going to kill your chances unless you did something like save someone's life, just got through signing autographs after your movie premier, or getting voted MVP of your professional sports league when you met her. Point is that you want her to feel seduced and your biggest advantage is keeping her caught up in the moment and not waiting for moments to become memories.

Also, quality girls are hit on every single day. Waiting gives the next guy a chance to beat you to the call.

Then when would be the good time? I came off a needy when I sent texts or calling the girl too soon. That is why I decided to change my tactic into the waiting game.

I find the best approach is let her know up front that you want to go out with her. You can try to get her to go out with you that minute when you meet her if possible. However, you can ask her out for your date during your initial meet...if she says yes, you set your date and time (next couple of days) and get her number just to follow up. Or you can tell her you want her number so you can call/text her about setting up the date (I prefer this).

The point is you are giving her something to look forward to rather than saying "Can I have your number" and leaving it at that.