Two answers:
First answer: Realistically it's a numbers game. If you try enough times just talking to women (a) eventually it will work, and (b) practice makes perfect. Just suck up the courage and do it, but know that you are likely to be shot down many times. Partly because you are going to fuck it up the first few times before you learn. Partly because it's a numbers game--you get shot down a hell of a lot more often than you get "yes".
Second answer: The odds are horribly against you if you walk up to a girl "cold" and just start chatting her up. You are MUCH more likely to succeed if you have an "in". That is, something in common. It could be that you have a mutual friend, it could be that you are both experiencing the same frustrating situation together. An "in" is something that allows you to start up a conversation naturally, because ANYONE in that situation would have had a conversation, because NOT having a conversation in the presence of the "in" would be weird. Like a friend introduces you--it would be weird NOT to have a conversation. With an "in" your odds are about 10 times better of getting a number.
In consideration of the overwhelming importance of the "in" the real trick is to set your life up to create the maximum possible number of "ins".
Literally what this leads to is some pretty simple advice: Chat up everyone. Not just for dating. Start conversations with strangers. Pretty women. Ugly women. Men. Anyone. Find topics, and start conversations. What this leads to is a lot of random situations where you are chatting with this ugly girl, or this guy, or whatever, and out of nowhere this hot girl comes along and joins the conversation. Welcome to your in. Basically you create your own luck by being as social as you can be with as many people as you can--sooner or later it'll lead to the conversation you really wanted.
The other plus to all of that is that by engaging as many people as you can as often as you can you are practicing your small talk MOSTLY in non-threatening situations, meaning, situations where you have nothing to gain or lose, so your stomach isn't crawling up into your throat. The skills you gain from generally engaging with everyone will serve you really, really well when that hot girl comes along and your stomach is doing back-flips--but you'll have some common topics and jokes and stories from all those other conversations, and you'll pull it off.