The practical core is the analysis of impressions. Something happens, an impression arrives carrying an implicit judgement, and the one thing genuinely up to a person is whether to assent to it. Emotions on this account are not forces that overwhelm reason but mistaken judgements about value: distress is the judgement that something bad is present, and it dissolves when the judgement is withdrawn. That is why the Stoics could hold both that everything is fated and that a person is responsible, since assent is the person own act even where the impression was not.
Only virtue is good and only vice is bad. Everything else, health, wealth, reputation, the lives of one own children, is indifferent, though the Stoics graded indifferents into preferred and dispreferred so that the system could recommend anything at all. The other half of the ethics is oikeiosis, the natural widening of concern from the self outward to family, community and the whole human race, which produced the Stoic claim to be a citizen of the world.
Almost nothing survives from the founders. Zeno, Cleanthes and Chrysippus, who between them built the system, are known through fragments and hostile summaries. What survives whole is Roman and late: the letters and essays of Seneca, the discourses of Epictetus written down by Arrian, and the private notebook of Marcus Aurelius. The modern revival reads those three, which is why it is strong on the ethics of assent and light on the physics that generated it.