Trying to figure out how old planets are is a very tricky science. The planets formed billions of years ago so it is difficult to appropriately estimate how old planets are, but scientists have been able to get pretty close. The Earth is about 4.54 billion years old with the age being potentially 50 million years more or less than that estimate. Scientists use the Earth's crust and rocks in order to help determine a rough estimate of the age of the Earth.
Scientists have even used helpful clues from outside sources like the moon or different meteorites to help accurately pinpoint an age for the Earth. When put into perspective in consideration of the entire universe into one year, humans have only been around since the last minute of the last hour of the last day. Pretty cool!
Scientists have been able to estimate that the Earth is around 4.5 billion years old. This estimate comes with a 50 million year plus or minus error range since it is impossible to actually pinpoint the exact number. Scientists have formed this estimate through a few different methods including the process of dating the rocks found in the Earth's crust, as well as studying neighboring bodies such as the moon and meteorties that have visited over time.
These methods have proven to be the most reliable methods. Some other past methods have not been as reliable such as studying the ocean tides and the time it took the Earth or the Sun to cool to current temperatures.
Approximately 6,000 years old. The Big Bang states that there was a big explosion and everything came to order. If you had an atom bomb in your hands detonating in 5 seconds, how sure would you be that you would be fine? Probably 0%. Point is, after an explosion, nothing is in order. Before the explosion, the Big Bang also states that it came from a clump of material. That brings up the question, "where did that material come from?" Currently, the young earth theory is the most reliable theory.