One of the things that distinguishes serious Stoicism from the popular self-help version is that it is not just a collection of practical tips. It is a complete philosophical system, and the practical advice is grounded in a metaphysics and a logic that are worth understanding.
The Stoics divided philosophy into three parts: physics (the nature of reality), logic (the nature of reason and valid argument), and ethics (how to live). They used the analogy of an egg: the shell is logic (the protective outer structure), the white is physics (the body of content), and the yolk is ethics (the center, the point of the whole). All three are necessary, and ethics rests on physics.
The Stoic physics is a form of materialism and pantheism. Everything that exists is corporeal, even the soul, even God. But the universe is not mere dead matter: it is permeated by a rational principle the Stoics called the Logos, or pneuma (breath, spirit). The universe is, in a sense, a single living rational organism of which all particular beings are parts. The Logos is identical with Zeus, with fate, with providence, and with nature. This is not personal theism in the modern sense, it is closer to what Spinoza would later call Deus sive Natura (God or Nature).
From this physics follows the Stoic attitude toward fate. Everything that happens is an expression of the rational structure of the whole, of the Logos. The Stoic slogan is amor fati: love of fate. Not resignation or passivity but a positive embrace of what happens as the expression of the rational order of the universe. Marcus Aurelius returns to this theme repeatedly in the Meditations: what happens is what nature requires; what nature requires is rational; resistance to what is rational is itself irrational.
The Stoic logic and epistemology ground their ethics in a theory of judgment. The Stoics distinguished between impressions (phantasiai), the raw presentations of experience, and the assent (sunkatathesis) we give or withhold to impressions. When something happens, an impression arises: "my reputation has been damaged." But the impression comes with what the Stoics call an evaluative tag: "this is bad." The Stoic practice is to suspend assent to the evaluative tag, to recognize that the evaluative component is not a feature of the impression itself but a judgment you are adding. The damage to reputation is an external fact. That it is bad is a judgment. And judgments are in your control.
This is the Stoic account of passions (pathē): what we call emotions, but what the Stoics thought of as mistaken judgments. Grief, fear, desire, and anger, in their pathological forms, all involve an implicit false belief about the goodness or badness of external things. The Stoic goal is not the elimination of feeling, that is the popular misconception that makes Stoics seem cold. It is the replacement of passion-based reactions with eupatheiai (good emotional states): joy (rather than pleasure-seeking), caution (rather than fear), and wishing (rather than desire). These are rational, appropriate responses to the world; they do not involve treating external things as if they were unconditional goods or evils.