Relative dating tries to determine the relative order of past events without determining absolute age. Therefore, relative dating does not use radioactive decay or half-life in order to determine the exact numerical age of a fossil. Instead, scientists that use relative dating try to put the rocks that are left behind by geological events in chronological order. This method is known as stratigraphy ("strata" = layer).
Most fossils are found in sedimentary rocks. During this process, the remains of the organism are buried by sediments and the bones become mineralized. Relative dating is based on the geological principle that sedimentary rocks are formed from bottom to top. Therefore, fossils found in the bottom layers, or strata, represent the oldest forms of life in that rock formation.
The link below describes additional geological methods that are used to date fossils and rocks.