I get nervous as well. A couple things to note..
What you say really isn't important. A lot of the time it's just small talk. I think people focus way too much on being a DON JUAN MASTER and saying the MAGIC CONVERSATION PIECES that are supposed to DROP THEIR PANTIES.
She showed you an IOI so now you have to IOI her, she IOD'd you so NOW you have to neg her, you have to do THIS thing at THIS point in the conversation, make sure you say THIS thing THIS way or it could be a DLV and she will drop you like a rock and hate you forever. That kind of nonsense.
These lines that "pua" people keep telling you are, for the most part, full of crap. I realize you're probably uncomfortable saying anything to these girls when nervous.
There's no magic words. Especially for a beginner, don't get caught up so much in trying to find the perfect thing to say. Just make conversation. Make sure you tell yourself that girls are quite forgiving, especially when they think you're shy. If they're attracted to you, like you said...they'll make it easy for you, so just try to take advantage of it. I know what this anxiety you're feeling is. It's like this wave that hits you and keeps increasing the more you stand there awkwardly, almost like a feedback response. Time seems to slow down and every second feels like an eternity. This is found in other areas in your life, such as when you're speaking and public and freeze up. What you need to do is come to terms with your fear and mentally calm youself. I know this is easier said than done. But work on mentally saying to yourself "i am fine. This will pass. I can control this and make it disappear." Maybe this is a bad analogy, esp if you've never done drugs...but its almost like you're tripping on shrooms or acid. You can control how hard you trip with your mind, and things can get scary if you start tripping too hard. But the way to conquer this is to
A) Go with it. Acknowledge that this is happening and you are feeling what you are feeling. This realization will make this fear less intimidating, and
B) Realize that you have complete control of your brain and how hard you're "tripping", this fear and paranoia can disapear simply by hitting a switch in your brain and making it go away.
There are a few things you can try: take a deep breath and just smile and look at her. If you make it seem like she is the one being awkward by not saying anything, in most cases she will simply start talking to feel the dead air. I do this all the time. It's a type of framing. If you frame it as her being the quiet one, she will adopt this reality, so long as you dont have a look on your face that gives away that you're thinking "God, i hope im not being awkward". Just pause, breathe slowly, and peer at her, not in a creepy way, but in one that makes it look like you're evaluating her and waiting for her to say something.
You need to work on not being outcome dependent. If you muck it up by tripping over your words...so what? Who cares? This is a good thing. Tell your self over and over again that every rejection is one step closer to becoming good with women. After a while it starts to numb you and you see that it doesnt really even matter. Once you cross what RSD refers to as the "indifference threshold", it gets much easier. Like anything, you have to fail over and over and over again to get good.
It also depends what situation it is. If you're at a party, my strongest advice would be to eject as soon as you feel yourself slipping. That way, you avoid saying anything weak and timid, and you get brownie points for walking away from her, because she assumes you're not going to just hang off her all night. She'll likely be there for a while after you stop talking to her, so you can bump into her again and resume. If you are doing a cold approach during the day it's different because you basically have the one chance to get the number before you bounce.
I understand it's hard to feel natural when you freeze up. I wouldn't even worry about kino if you're real nervous, it's likely just going to come off as forced. One thing that really helped me is become friends with good looking girls and spend time with them to get used to being around them and socializing. That's right, get in the friend zone on purpose. Once I got good friends with this entire apartment of girls, and after constantly hanging out with them and listening to them complain and fart all the time and say stupid stuff, it takes this mystique (the Pedestal) away from girls and you start to see them as just another dude (sortof). Obviously don't hang around girls you have massive crushes on cause that will just drive you nuts.
Hope this helped a bit
