Fate gets a lot play in Stoic circles, and we even use it to poke fun at our fellow philosophers, the Cynics. It starts out with a typical Cynic-style chreia.
On a road there is a dog tied to the cart. The dog cannot help being tied to the cart, it is merely the situation as he finds it. The cart begins rolling down the road, headed to some destination or other. The dog has two choices: he can fight against the rope and cart, pulling, getting dragged, yelping, and struggling; or, he can trot along side the cart to wherever it is going.
Regardless, the dog is going where the cart is going. There’s no helping that. The only choice is whether he goes willingly, and thus makes it easier on himself and more enjoyable, or he gets dragged biting, snapping, and pulling the whole way.
This is the Stoic conception of Fate, generally. Now, we as modern practitioners tend to break it down into a few more types and genera. We can view Fate as the chain of causes across the whole cosmos which is cause => effect. If a thing is dropped on Earth, it is fated to fall, generally (unless it’s nature is otherwise, like helium). It is a simple, mechanistic view of the universe. This is the modern, atheist view.
Some might view Fate as the will of God, or the cosmos. Nature’s Providence. The “good end” to which all this is moving. This would be the theological view. Some others view Fate as a force itself, something if not godly, then at least worthy of being capitalized.
So how does fate and nature and our choices all mesh?
Another chreia, then:
A cylinder has a certain nature for roundness. And when it is pushed, it rolls. The cause is the pushing, but it’s nature determined what happens. The cylinder rolls while the block slides. Similar causes, affected by their nature, yielding different results.
Causes yield effects. This is made more complicated as rational creatures are causa sui or ’causes in themselves.’ Namely, we have some measure of free will which is also a cause. Unlike the previous example, we are both the shape and the push. We have a certain amount of flexibility, to be true to our nature or fight against it. To push, or to be inert.
As rational creatures we are a causa sui.
(This accpetance both of determinism and free will is called Compatiblism, more here.)
To my mind, a mixing of the two main camps is the better thought model:
An unending chain of universal causes from the beginning of time has been shaped to provide *me* (and you), with the opportunity for virtue. We are not enslaved by the vicissitudes of Fate, no. It instead provides us with the situations, contexts, and possibility to exercise the greatest value humans are capable of: excellence.
So, how can we, in the face of this cosmic test, do anything but try to meet it with the best we have to offer? That is our Fate… if we choose it.
Mountain Stoic 
What do you think of this idea: By choosing to act virtuously we can change our nature. We cannot change the mechanism of Fate, but the raw material it uses we can.
By way of analogy, under our control is the choice to be a virtuous, say, cylinder, or a non-virtuous cube. We cannot, however, control outcomes — how Fate disposes of us. So our choices to be virtuous can affect Fate indirectly, not because our Fate will change, but because a better Fate will come to us dependent on our nature (which is under our control).
In simpler terms it’s as if we have a tertiary benefit of increasing our chances of a good outcome by living the good life. For example, even though our preparation, skills, character and virtue make us the best fit for a job, another applicant who is a worse fit could be chosen in the end regardless. But we are indeed better off internally first of all, and second of all more likely to attract work that is fitting with our value by having those qualities than by not having them — their absence would cause us to be dependent on Fate to happen to drop a good job on our heads.
“Man’s character is his fate.” – Heraclitus, Fragments