They didn't. Electrons and orbitals were not discovered until much, much later. The electron was not discovered until 1897, and the shell model of the atom, and the notion of the valence bond, was not proposed until the early 20th century.

Chemistry in the 18th century did not rely on any of these concepts whatsoever. It did have the idea of atoms, which was a hypothesis and not something discovered through rigorous experiment. But it was a useful hypothesis, and one that could help make sense of some of the kinds of reactions that chemists and alchemists had been working on. They also, from this idea, had the idea of molecules (collections of atoms), and began to conceive of chemical reactions as just rearranging these atoms. But they had to infer all of this from experiments — looking at the inputs, looking at the outputs, and trying to figure out what had happened. Even identifying what the inputs/outputs accurately was very difficult prior to spectroscopy.

The Chemical Revolution of the 18th century, in which chemistry got much more precise, the concept of atomic theory began to influence how chemical reactions were understood, and the fact that there was a plethora of different types of elements, is fascinating in part because it was done by people whose knowledge of physical atomic structure was essentially nil.

They did have some technology, if you consider the standard tools of chemistry — retorts, distillation, fractionation, etc. — to be technology. But the major advances were not technological but conceptual. The big names here, if you want to investigate their work further, are Priestly, Lavosier, and Dalton.