What - according to Epictetus - is a Stoic? A person who knows that some things are within their control and some things aren't; a person who can change the things that are under their control and reconcile themselves to the things that aren't; a person who understands that their important possessions cannot be taken from them unless they choose to give them up.
What could these possessions be? It varies from Stoic to Stoic - feel free to choose your own - but they've got to be ways of using impressions. Good health and riches are merely impressions from the outside world (things that aren't part of us), and don't qualify as important possessions, but inner dignity and calm are ways of using impressions and do qualify. In theory, you can maintain calm no matter what happens to you; and if you don't, then you (and only you) have decided to give your calm up. You can't maintain your riches no matter what happens; they're out of your control, and so don't really belong to you.
Epictetus' way of doing this is to practice equanimity. When you come into money, he advises, say to yourself: it has come to me from the world, and may soon leave me. When your child is born, say to yourself: this child is mortal, and may soon die. If such a thing happens, you'll have prepared yourself and will be able to retain your virtue. This doesn't mean being insensible to worldly pleasures - you're free to enjoy your money and love your children, of course - but a proper Stoic maintains a certain level of detachment.
A central belief of Stoicism is that emotions and desire are fully within our control. If we say that we were 'carried away by lust', or 'consumed with anger' and not responsible for our actions, a Stoic would chuckle and call us a liar. This contradicts the established Freudian view of emotions being 'bottled up' and needing to be released. If you clamp down on your anger, the Stoics say, it won't fester and eventually erupt; on the contrary, it will fade with time and you'll become a less angry person. My personal experience, incidentally, leads me to side with the Stoics over Freud.