Fossils almost never contain DNA. So how can we know how closely or distantly related fossil organsims are to living organisms

While it's true that Fossils hardly even contain DNA, they can still provide numerous clues in order to identify and verify an organism.

For example, in terms of Dinosaurs, their bones and fossils have provided enough evidence to provide an evolutionary link with modern birds.

Carbon dating is another way to find the age of a fossil which provides more information on it's surrounding habitat and the animals it interacted with.