How long have they known each other? How often do you think they send letters to each other? What evidence in the text is there to support their relationship?
Ophelia tells Polonius that Hamlet has made many honorable declarations of love to her. Polonius pooh-poohs these declarations, saying, much as Laertes did, that Hamlet wants nothing more than to assail her chastity and then leave her.
In Act III, Hamlet catches sight of Ophelia. After a short conversation she attempts to return some of the remembrances that Hamlet gave when courting her. Hamlet replies caustically, questioning Ophelia’s honesty. He then berates Ophelia, telling her off sarcastically and venomously, with the refrain, “Get thee to a nunnery,” or in other words, “Go become a nun to control your lust.” After this tirade, Hamlet exists, leaving Ophelia in shambles.
We can safely assume Hamlet and Ophelia exchanged letters while he was at the University. They've known each other for a long time, possibly since they were children.
