How do we know that we have isolated a substance?
While modern tools make this easier, there are plenty of physical characteristics that help identify that a substance is pure

Modern tools like NMR, X-ray structure determination and others make identifying pure substances and their structures relatively easy, there are plenty of other characteristics than can support the identification of a pure substance.

Pure compounds tend to have sharply defined boiling points or melting points, for example. So if you can generate crystals, that is a good start. Crystallisation from solution, for example, tends to yield relatively pure compounds and this can be checked by measuring the melting point. Repeated fractional crystallisation can confirm this if the melting point doesn't change. For liquids you can distill them and observe the boiling point. Fractional distillation can separate mixtures and you can check that the results boil at a single temperature. Gases also have physical properties that can be checked after fractional distillation or other separation techniques.

Here is an example where attention to detail yielded the discovery of a new element. Rayleigh and Ramsay were experimenting with the separation of gases and noticed that nitrogen isolated from air (by removing all the other known gases) seemed to have different properties to nitrogen formed from chemical reactions (it was about 0.5% denser, for example). By careful fractional distillation, Ramsay was able to isolate a much denser gas from the nitrogen which we now call Argon. This was verified to be an element by observing its discharge spectrum which had new lines in it not present for other elements. So careful separation techniques and carful observation of physical properties could yield a new substance with different properties to nitrogen.

Before we had modern instrumentation this careful application of known chemical and physical techniques was the basis for the development of the laws of chemistry and the identification of new pure substances. It takes more time, but it works.