The earth is about 4.54 billion years old. This is not a theory but is a scientific fact. The science behind this fact is not that difficult to understand. Estimates on the age of the earth come from the radiometric dating of materials (rocks) to discover the amount of radioactive decay that has occurred since the materials being "metered" were sequestered inside the rock.
See the related question on uranium-lead dating. It is fairly easy to read and makes it easy to "connect the dots" and get an understanding of the ideas.
The most recent data indicates an age of 4.567 billion years.