What kinds of evidence do scientists use to them classify organisms? how does taxonomy us understand relationships among organisms on earth?

Physical, as well as genetic evidence, are used by the scientists to classify organisms.

Physical evidence may involve structure comparison such as fossils, homologous and analogous structures, vestigial organs et cetera.

Genetic evidence includes the comparison of genetic material, that is, the similarity in the DNA sequence.

Taxonomy helps us to understand that how close one organism is from another. For example, the vertebrates are more closely related to each other as compared to the invertebrates. In addition, it also supports the idea of common ancestry.