How do scientists determine the age of ancient artifacts that were made out of organic material? Well this question used to boggle my mind as well until I learned about Carbon Dating.
First of all, what is carbon? Carbon is an element that has 6 protons and usually 6 neutrons. The atomic number of carbon is 6 while the atomic mass of carbon is approximately 12. If carbon has 6 or 7 neutrons, it is considered to be stable but if it happens to have 8, then it is radioactive.

When carbon is radioactive, it decays into nitrogen; its half-life is 5,730 years. Which means if there are 12,000 atoms of radioactive carbon, after 5,730 years, there will only be 6,000 radioactive carbon atoms, and 6,000 nitrogen atoms.
All living things are made out of carbon because it is one of the most plentiful elements on this Earth. If an organism is living, then the amount of radioactive carbon stays at a constant. The moment that organism dies however, the carbon starts to decay.
Scientists observe how much carbon is left in something to estimate how many half-lives it has been through. By knowing how many half-lives have passed, scientists can get a pretty accurate estimate of the age of an object.
Carbon Dating only works on organic material like wood, animal skin, animal bones, and actual animals themselves but it will not work on stuff like rocks, water, or metal.