The Earth was made about four and half billion years ago, along with the rest of the solar system. The whole solar system used to be just a cloud of matter (mostly hydrogen), which collapsed under its own gravity. A bunch of the hydrogen gas collapsed to form a star, which is our sun; the rockier junk stayed in orbit around the sun, and over time that junk collided with itself over and over again until it formed the rocky planets, including the Earth. In fact, we think that this is how pretty much all planetary systems form.

The Earth is 4, 568,000,000 years old. And you thought your dad or grandpa was old!

Our solar system formed between 4.7 and 4.5 billion years ago. This number is taken from the ages of meteorites, because we can determine the ages of individual rocks. No rocks on Earth are more than about 4.0 or 4.1 billion years old (apart from meteorites that have fallen to Earth, that is); however, geologic processes on Earth tend to destroy rocks and so rocks even 4.0 billion years old are very, very, rare. It is generally thought that the Earth is about as old as the rest of the solar system, but that the rocks on Earth older than 4.0 billion have been destroyed by erosion, melting, etc.