I know that there are certain norms in Islam that has to be followed while meeting people of the other sex. Now in situation when you are to decide whom to marry, how do you go on discussing this issue with the opposite sex so that the meeting remain within the norm of Islam?
Different muslim cultures have different rules ('urf) for how separated men and women are to be. Shaykh Hamza Yusuf has commented that he has friends in western Saudi where the wife eats with them and they all know each other, and he has friends from eastern Saudi that he's known for 20 years, and has never met their wife. Different strokes.
Still, a male and female are not to be alone together. If by dating you mean old style courting, where the male and female speak politely with a chaperone, this would be allowed by many opinions (but not all! I recall reading in The Reliance of the Traveller that a woman is not to talk to a non-mahram, even to reply to his salaams).
A common thing (or so I've heard) that they do (in Egypt specifically) is when the prospective couple meet (with a chaperone) and decide to take the next step, they do nikah. Islamically, they are now legally married, but for their (cultural) purposes they are just engaged, and they start "dating." In this case, dating would of course be halal, since they're technically married. Then later they have the walima (marriage reception), which they (culturally) consider to be the actual marriage and that's when the wife will actually move in with the husband.
Or so I've heard! And God knows best.
Hmmm a nice question and a nice and suitable background!
Well according to Islam, a man is not allowed to meet a woman in person. But when it is the matter of their marriage such as you are describing. Like they are engaged or are to be engaged to each other and want to know more about each other.
Then it is allowed for them to talk and know each other. But to keep in mind, they should stay in the limits! They should just know each other such as their nature, their likes dislikes!
And should give their acception or rejection in answer!
However, dating is not allowed! What you might wanted to ask was the meeting of the man and woman, who are to married and want to know more about each other.
There is nothing bad or evil, in a meeting of man and woman. But the purpose should be positive and there shouldn't be any sin involved. Their families should know! A girl before leaving her house should inform her parents and so on. It should not be kept hidden!