Stoic ethics has two pillars that are worth understanding clearly: the theory of virtue as the only good, and the practice of memento mori and negative visualization.
The Stoics held what is, by contemporary standards, a radical position: virtue is the only genuine good. Not health, not wealth, not fame, not pleasure, these are what the Stoics call preferred indifferents (things it is rational to prefer, all else equal, but whose presence or absence is not relevant to your happiness). The only thing that is genuinely good, that genuinely makes a life go well, is the condition of your rational character: your wisdom, your courage, your justice, your self-control. A person with perfect virtue who is also ill, poor, and socially outcast is, on Stoic doctrine, living an excellent life. A person of vicious character who is wealthy, healthy, and celebrated is living a bad one.
This seems absurd until you consider the alternative it is responding to. The ordinary view that happiness requires external goods makes your happiness permanently hostage to fortune. Wealth can be taken. Health fails. Reputation fluctuates. Loved ones die. If your wellbeing depends on any of these, you are permanently vulnerable. The Stoic counterproposal: make your wellbeing depend only on what you cannot lose, your rational character. This is not resignation to poverty or ill-health. It is a principled restructuring of what you take yourself to be fundamentally depending on.
Stoic cosmopolitanism follows from the shared Logos: if all rational beings partake of the same rational principle, then all human beings are, in a fundamental sense, fellow citizens of a single world-community. Marcus Aurelius was Roman emperor, but he wrote in his journal that he was first a citizen of the world and second a citizen of Rome. This was not rhetoric, it was a philosophical commitment with practical implications about how to treat people who were not Roman, not citizens, not one's immediate community.
The Stoic practices are what make the philosophy live rather than remain abstract. The most important:
Negative visualization (premeditatio malorum): regularly imagining the loss of the things you value, your health, your loved ones, your work. Not as an exercise in misery but as an inoculation against taking these things for granted, and as preparation for loss when it comes. Seneca writes: imagine this is the last time you will see this person, eat this meal, watch this sunset. Gratitude and equanimity follow from genuinely doing this, rather than from the common but deluded strategy of refusing to think about loss.
The view from above: a meditative practice of imagining yourself rising above your current situation and viewing it from a cosmic perspective, from the perspective of the whole of human history, or the whole of the cosmos. Personal slights, failures, and anxieties look very different from far enough away. Marcus Aurelius uses this repeatedly: think of all the emperors before you who thought their affairs were permanently important. Where are they now?
Daily examination: at the end of each day, Seneca writes, review what you did and said. Where did you fail? Where did you succeed? Not with self-flagellation but with honest appraisal and a commitment to do better tomorrow.