It could be a very short time or a long time, depending on the situation and local customs. It is allowed for a man and woman to see each other for the purpose of engagement. They can also find out more about each other through their relatives and mutual friends. However, it is haram for the engaged couples to be alone with each other. Engagement is not marriage and until nikah is performed they are not halal to each other.
Engaged people can talk to each other on telephone.
They can also write to each other and they can meet in the presence of other adult relatives. I read your column in Pakistan Link regularly. May Allah give you the reward for the services that you are rendering to the Muslim community. I have a question about which I am really confused. Would you please clarify it.