Archaeologists use the help of a wide range of physical sciences in determining ages.
This can include a variety of radiometric dating techniques, but there is a lot more.
Stratigraphy, that is, soil layers, can be a great dating tool as well. Some events show up quite clearly in soils. For example, in the Pacific Northwest ash from the Mt. Mazama eruption ca. 7,000 years ago shows up clearly in a lot of sites. Layers above that ash are <7,000 years old while laters below that ash are >7,000 years. That is just one very simple example.
Pollen is another tool. Over time as climates change, so do the vegetation communities. Examining pollen can help to establish general ages. In some cases pollen can be radiocarbon dated, providing more precise ages.
Cultural sites can be dated by artifacts and other time stratigraphic markers. Time stratigraphic markers? Here's an example: back about 40-50 years ago beer and soda cans had pull tabs, and they were made of aluminum. People pulled them and discarded them by the millions. In a few thousand years those pull tabs will be a perfect time stratigraphic marker as they are very durable, very widespread, and lasted for a very short time. Archaeologists use various stone, bone, and shell tools--and occasionally other items--in much the same way to establish dates.
Here's another example; the Piltdown fossil find was originally thought to be real, but it was finally disproved by a type of dating that showed that different pieces were of considerably different ages. That method didn't establish a precise age, but did show that the various pieces were of different ages. That's called relative dating.
There are a lot of books, and a lot of good articles you can find on the web if you avoid the creationist sites. And we have several experts here on EvC who can probably answer any specific questions you might have.
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.