First and foremost, congratulations to you! What a joyous path of discovery you are on!
I heard a wonderful homily about this recently. You may be feeling nervous because often, when a young man or woman tells someone that they are being called to religious vocation, the response can be unintentionally negative.
The priest who gave the homily pointed out that the response often (and nearly immediately) brings up the matter of "sacrifice." As such, the young man or woman might feel defensive about something that they shouldn't have to feel defensive about.
Like RNesbit said, you'll probably feel more comfortable if you bring it up with casual confidence. Even if your family is Catholic, you may well get the "Oh, but that's such a big sacrifice" line. You can, of course, remind them that any path that a Christian chooses requires sacrifice. If you were to hold a non-religious vocation and get married, would that require any less sacrifice? Certainly not. It would simply be a different kind of sacrifice, that's all.
Since our life in Christ is about pleasing God, I am sure that your family will come to understand your calling. Of course, there may be no objection, and they may understand right away, and respond with great joy.
You have my prayers. Please keep us posted on how it goes!