So there’s a cute girl I work with (they all begin this way, don’t they :)? I want to ask her to lunch but I don’t want to just walk up to her and say “Hey, wanna get lunch?”. Instead, I’ve been reading “How to Win Friends and Influence People” and want to see how well some of the advice in that book works. I want to have some fun and see if I can influence the situation into having her ask me to lunch instead. So, who has any thoughts on how to go about doing this?
Hmmmm, you want to influence her into asking you out ? Are you gonna use your powers to get her into bed too?
I’m really curious… How old are you ?
I have no thoughts on how to do what you propose, but if you think you have a chance, just ask her, or, hey, ask her to ask you !
If I remember that book correctly merely modify your sentence to start with her name and smile 
Was the book not any help?
The point of the book is to modify your thinking so that people more naturally like you. It will not get her to ask you out, the best you can hope for is that she will enjoy your company and be positively inclined to get lunch with you.
One of the things to remember is that the strategy was not really designed to “get you things.” Mr. Carnegie thought very poorly of people who said “what did you expect to get” when he related a particular story about a postman. He never expected to “get” anything, he was just being pleasant and likable. If you are trying to have “fun” with her, you are not really getting the point of the book.
Be nice, show a genuine interest in her, and follow the book’s advice.