Determine the amount of Carbon-14 in the fossil. From this, you can determine its age by calculating how many times it would have been reduced by half. It there no Carbon-14 in the fossil, it is probably too old to date by this method. Carbon-14 dating is limited to fossils up to about 70,000 years old. If the fossil is older than that, you'll need to use a different method, which measures the age of the rocks associated with the fossil, instead of analyzing the fossil itself.
Choose the method of dating you will use and obtain the rocks that were found around the fossil and that can be used for dating it.
Calculate the age of the rock surrounding the fossil. The most common method of dating rocks to find the age of a fossil is to examine the ratio of Potassium-40 (parent) to Argon-40 (daughter). The half-life of Potassium-40 is 1.3 billion years. The rock must be at least 100,000 to 500,000 years old for this method to work. It can be used from that time to the age of the Earth.
You should now have the age of your fossil. There are a few other techniques using elements with even longer half-lives if you need to continue.