Information based on Wikipedia.

About 2 1/2 million years ago, people were living in the part of the world we now call Egypt.  About 10,000 years ago they tuaght themselves to hunt and gather food. Before that they ground grain to eat. Then about 8,000 years ago, we don't really know for sure why, the land got dryer and dryer. Eventually it turned into the desert we now call the Sahara. The people who live in the areas that dried up moved (migrated) towards the river and settled in the valley bordering the Nile River. Instead of hunting and gathering, they taught themselves to plant crops.  The tribes started to farm.

It's still very hard to figure out exactly what happened since there is so little evidence from that long ago. But according to some it looks this.

The early settlements were in the Upper Nile, in what is now Sudan and Libya. Scientists have made up names to be able to talk about the tribes before the first king, which the Egyptians to be called a Pharoh. You can find a scientific description of the names and a timeline here

 Sometime around 3000 BC, the many tribal settlements along the Nile started to interact with each other. Various small "city-states" started to form along the Upper Nile. According to scientists, the three biggest ones were Thinis, Naqada, and Nekhen  and by around 3150 BC, lead by  King Menes, they created Unified Kingdom. This was the beginning of the rule of various kings  that ruled Egypt for the next three throusand years. 

The people who lived under the ruling families didn't call their land Egypt. At the time, the scientists believe they called themselves  either tAwy, meaning 'Two Lands'; and later km.t  KÄ«mi), the 'Black Land', a reference to the fertile black soil deposited by the Nile when it overflowed its banks and in the Delta area. Meanwhile, the families are called dynasties.

One story about the Pyramids and the Sphinx from http://www.mysteries-in-stone.co.uk/index.htm

Egyptologists ( scientists who study Egyptian history) believe that the Sphinx and pyramids were built around 2500BC, but some of them believe that the Sphinx is much older and even were built before there were people who called themselves Egyptians. The Sphinx is carved from a natural outcrop of limestone. It is believed that the Sphinx is the earth image of the constellation Leo in the heavens at around 10,500BCE. A geologist did some research on the Sphinx and he believes that the erosion of the body was done by rainwater and not by sand. He believes we should be looking to times before 3000 BCE because of the extent of the erosion. He has said that the extent of the erosion indicates to the dates between 7,000  10,000 BC for the body. The head however though damaged is not as eroded as the body, is smaller in dimension compared to the body, and has had extensive work done to it over the millennia.

The pyramids are supposed to represent the belt of Orion, another constellation and that they are of the same age. Egyptologists strongly dispute these claims as preposterous. The structure of the Pyramid was invented by Imhotep, the chief architect of Djoser (circa 2,700BCE) He discovered how to make a tomb for his king in whose appearance would symbolise the ascent of the soul. The result was the step pyramid at Saqqara, a pyramid with 6 steps. Imhotep was later defined as the patron saint of scholars. The 4th Dynasty’s first Pharaoh was Snofru. He has three Pyramids at two sites, one at Maidum and two at Dashur.

The Pyramids of Khufu (Cheops), Khephren and Menkera dominate the Giza Plateau These are a fabulous legacy to the reign of these three Monarchs of the 4th Dynasty.