OK dude, I suggest you read up on some material and go out! Specifically read up on The Attraction Code by Vin DiCarlo and the 60 Years of Challenge books. As you're reading those go out and meet some girls.
Remember to only focus on what YOU CAN CONTROL, not anything else. What can you control? What you want, your actions and words. State your intent. Know what you want and be congruent to that all the way through. Never apologize for any of it. You're not so good with words? No matter, most of it is body language and vibe anyway. You could literally be talking about the weather and yet still have sexual attraction behind the words. All you have to do is not apologize for any of it. Be unapologetic.
So onto the approach: This is something COMPLETELY within your control. Of course you might get Approach Anxiety, but that's because your focusing on the outcome, on the reaction of the girl. Instead focus on what you can control, which is walking up and stating your intent - "Hey, this is gonna be really random but I saw you from over there and thought you were really cute, and I just had to come and say hi." Bam. Done. If she gives you a nasty response, or a response you hadn't expected, no matter. You did what you had to do and that's all that matters. Keep ploughing through if possible because that you can also control.
If she gives you a good response you're golden, at least for now. You have to initiate the escalation. Which once again is also in your control. With escalation I mean both physical and the vibe. Verbal as well. Physical escalation can be found under the Vin DiCarlo Escalation Ladder, the basics are going from incidental touching to overt touching, starting with shoulders, hands, etc. Building up to longer touches where you hold for a few seconds, then let go. Then move to the back and legs and hips. Then escalate to a kiss. Also consider playful touching, such as thumb wars, which can be childish fun, but also generate sexual attraction.
Your eyes are also a tool for building sexual tension - eye-fuck her - meaning look at her and imagine fucking her. Don't apologize for it.
Remember to only focus what you can control.
Conversation - as said before, conversation doesn't really matter. Therefore SAY WHATEVER THE FUCK YOU WANT. Really do. Remember what you want out of this. You want to meet her. State it. Something about her caught your eye - got nice legs? Mention it. Her style? Talk about it. She looks creative or businesslike, or maybe artsy and gothlike. Say it. She looks like a rocker girl. Tell her. Then ask her what she does. Where she's headed right now (for daygame). Get to know her man. Who is she? Where's she from? Tell her where you're from. Get her to invest a little. Ask open ended questions such as Why did you move here? Or where would you like to move to in the future? If she studies something ask her if that's what she always wanted to study (hint, most of the time it's no, but sometimes it's a yes). Then tell her to tell you what she really wants to do with her life.
A few key topics:
Her name
Her style
What she's doing right now
Where she lives
Where she would like to live
Travel
Cooking - What's her favorite food? Can she cook? Let's have a cooking competition girl! The loser buys the other a drink...or something like that.
What she studies - what she really wants to do
Creativity
Movies - Is she a movie buff?
Music - Does she like good music?
You want to see her again
Pull out your phone
Tell her to type in number
What's her favorite drink?
Coffee or tea?
I'll give you a text and we'll hang out.
Hug.
So remember to focus on what you can control, which is getting what you want. Know what you want a go for it. Do you want to take her home now? Do you want to take her on a date the next day? Do you want to spend more time with her right now? What you want push for it. Get to no. Be playful and honest and truthful in the moment. That's all you can do, really. Being honest and congruent to what you want and going for that. And there is never a need to apologize (unless you harass the girl, but get close to it!

) Don't take her shit if she gives you any. Just stay congruent, tease her a little bit if she doesn't meet your expectations, and tease her for testing you, too. Have fun here. Lead all the time. You are responsible for anything and everything that happens, you must be to blame, so take the blame, do it.
Good luck.