In Act III, scene i, Ferdinand and Miranda decide to get married. This is exactly what Prospero had planned. Miranda, isolated on a desert island, has never seen a young man. Prospero arranges for Ferdinand to be the first male that his daughter sees, rightly predicting that she will be charmed at first sight.
Miranda, having no idea of the ways of the world, doesn't realize she should hide her feelings, play hard to get, and let the man do the proposing. She simply states plainly what is on her mind, stating to Ferdinand:
I am your wife, if you will marry me.
If not, I’ll die your maid. To be your fellow
You may deny me, but I’ll be your servant
Whether you will or no.
Luckily for her, Ferdinand, unlike some of the other men shipwrecked on the island, is a man of honorable character. He is honest and good, so he doesn't take advantage of her naive openness about her feelings.