Fossils almost never contain dna. so how can we know how closely or distantly related fossil organisms are to living organisms?

Firstly, similarities in physical features are determined; such as determining homologous, analogous and paralogous structures. Thereafter, chemical tests such as radiometric, relative or absolute carbon dating could be used to tell the age of the fossil. By comparing the anatomies of both modern and extinct species, paleontologists can infer the lineages of those species. This approach is most successful for organisms that had hard body parts, such as shells, bones or teeth.