Many paleontologists use both stratigraphy (The study of rock strata, especially the distribution, deposition, and age of sedimentary rocks.) and observations of the fluctuations of the Earth's magnetic field, which leaves different magnetic fields in rocks from different geological eras. Also index fossils found alongside the dinosaur fossils can give a clue to the era the animals lived/died in. However the accuracy of the time scales involved ultimately depends upon radio-isotope dating of the igneous (or volcanic) rocks above and below the sedimentary rocks that the fossils are found in.
For example, if a fossil is found in between two layers containing igneous rock dated to 70 million years and 80 million years respectively, the dinosaur must have died at some point in between those two times.
The reason we know radio-isotope (or radiometric) dating is fairly accurate is because we know that radioactive isotopes of elements, such as Uranium-235, decay at constant, known rates over time (its half-life, which is over 700 million years). We know this is true because scientists have measured it and found it to be true (a fact) Their results have been published, and the experiments repeated time and time again with the same results (this is how scientists test if something is true or not). An accurate estimate of the rock's age can then be determined by examining the ratios of the remaining radioactive element and its daughters.
Carbon dating is not used for dinosaur bones as the half-life of C-14 is only 5,568 years. Therefore, carbon dating can be only used for dating things 50,000 to 60,000 years old, much younger than the dinosaurs, which existed over 65,000,000 years ago.