I read the Handbook of Epictetus. It's very brief, just a few pages really. I'll quote a few paragraphs that should make it clear what Stoicism is about. (I'm quoting a recent translation by Nicholas P. White which I really like. The translations I found on the Web seem stilted, or florid, by comparison; though Higginson isn't bad. Of course you can try the original Greek.)
Some things are up to us and some are not up to us. Our opinions are up to us, and our impulses, desires, aversions—in short, whatever is our own doing. Our bodies are not up to us, nor are our possessions, our reputations, or our public offices, or, that is, whatever is not our own doing. (1.)
You are foolish if you want your children and your wife and your friends to live forever, since you are wanting things to be up to you that are not up to you, and things to be yours that are not yours. (14.)
If you are fond of a jug, say “I am fond of a jug!” For then when it is broken you will not be upset. If you kiss your child or your wife, say that you are kissing a human being; for when it dies you will not be upset. (3.)
Do not seek to have events happen as you want them to, but instead want them to happen as they do happen, and your life will go well. (8.)
The best of it is extremely well said, but the content is troublesome. If the sample above does not convince you that you should prepare yourself to be unperturbed when your wife and children die, then the rest won't either. Still, given that you're reading this, something of Stoicism is very likely in you. It's in Western culture.
I guess none of the quotes I picked addresses the evident problem of whether a Stoic may act, or whether he must be distant and docile at all times. The Handbook doesn't seem to offer a head-on answer. Modern Christianity's interpretation of Stoicism does, though.
God, grant me the serenityto accept the things I cannot change;the courage to change the things I can;and the wisdom to know the difference.—Reinhold Niebuhr, around 1944.
The wisdom, that is, to know what is up to us and what is not up to us. It is exactly this wisdom that is on offer in Epictetus: nothing is up to us except how we see things and how we comport ourselves. I think I like the modern Christian philosophy, demanding as it is of courage and wisdom, better. But then, I tend to like messy, perilous things in principle even when they are not so enjoyable in practice.
The Wikipedia article on the serenity prayer offers this lovely postscript. I have no idea why this rhyme is not a widely-known classic.
The philosopher W.W. Bartley juxtaposes Niebuhr's prayer with a Mother Goose rhyme (1695) expressing a similar sentiment, but without comment:For every ailment under the sunThere is a remedy, or there is none;If there be one, try to find it;If there be none, never mind it.