Vaisheshika starts from a question that sounds modern: what are the basic kinds of thing there are, and how do they combine into the world we experience? Its answer, laid out in Kanada's Vaisheshika Sutra, is a short list of categories, substance, quality, action, generality, particularity and inherence, later joined by a seventh, non-existence, meant to be exhaustive. Every dispute about what exists can in principle be settled by asking which category a thing belongs to.
The substance category does the heaviest lifting. Vaisheshika holds that the four material elements, earth, water, fire and air, are ultimately built from indivisible, eternal atoms, paramanu, too small to be perceived on their own. Two atoms combine into a dyad, three dyads into a triad, and so on upward until the compound is large enough to see, smell or touch. It is one of the earliest systematic atomisms anywhere, built to explain ordinary physics rather than to speculate about it.
What keeps the system from being pure mechanism is adrishta, the unseen force. Atoms combine and separate according to law, but adrishta, the accumulated and largely invisible residue of a person's past actions, is what nudges particular combinations to occur in a morally ordered universe rather than a random one. It is Vaisheshika's version of karma, doing quiet metaphysical work behind an otherwise strict natural philosophy.
The system did not stay separate for long. From around the eleventh century, Vaisheshika's categories and Nyaya's logic and epistemology were increasingly read as one combined project, Nyaya-Vaisheshika, in which Vaisheshika supplied the furniture of the world and Nyaya supplied the tools for reasoning carefully about it.