I have invited a girl on a date in a restaurant. I've ordered for our meals but I don't know how to start a conversation which will lead to a situation where I will ask her out.

I don't understand.If you are already out why would you be asking her out?
Explain please.
As an aside,I have never liked a man to give my order to the server.

I mean, I want to ask her to be my girlfriend

There is a time and a place for these talks and I am not sure that the setting is right.
Perhaps after dinner you could go for a walk and ask her if she sees any future for the two of you.
Say* I really like you and I was hoping we could be exclusive*.

How well, and how long have you known each other? Is this a first date? How old are you both? Do you work together? Where did you meet??

I agree that this isn't the appropriate setting for this question. What if she says no? Then you are sitting there eating dinner with awkward silence. Ask her on a walk, or on the ride home, or somewhere you two are alone and can discuss the idea.

Unless you are in a country where it's tradition, let the woman order for herself. This shows that you are controlling, and that she's not capable of making her own decisions.

All the above questions are detrimental to accurately answering your question.

You would probably want to ask her 'out' after dinner while taking her home or like suggested before go for a walk after dinner, somewhere more private where you two may talk easily and comfortably. Also if this is just your first date I would suggest maybe putting asking her out off to the side for a later date, she might think your rushing into things and could possibly scare her off!