Around 7 million years ago, the African ape Sahelanthropus tchadensis, the common ancestor of chimps and humans, came into being, diverging from the rest of the "Great Apes" which also included orangutans and gorillas. The Great Apes all exhibit forms of culture and communication beyond just their own bands or tribe, and can engage in behaviors such as empathic social deception, suggesting a theory of mind. Sahelanthropus tchadensis is considered the oldest hominin ancestor related to modern humans. Hominins include both chimps and humans while the genus Homo refers to human ancestors after the divergence from chimps.
Around five to three million years ago, human ancestors diverged from chimps with the species Australopithecus afarensis, of which the famous Lucy fossil is an example. We are sketchy on the exact dates because there is little fossil evidence of chimps, as they lived in a rainforest environment where bones are not preserved well. Sometime around 3 million years ago, our ancestors left the rainforest and started to colonize the plains, kickstarting many adapatations such as bipedalism. Australopithecus was the first group of human ancestors to walk upright.
Homo habilis, the first member of the genus Homo, lived 2.4 to about 1.5 million years ago, and was the first tool-user. The use of simple, one-faced stone tools decreased the load on the teeth, and the molars shrunk accordingly. Social organization became more complex, with larger bands on average, permitting mutual cooperation but also intense intra-species cooperation for mates and dominance. Spear throwing developed, and as game became more scarce, members of Homo were forced to migrate around, even leaving Africa around 2 million years ago when the Sahara became even drier and larger than usual.
One of the biggest drivers of human evolution was sexual selection and violence - if one band of early humans could assault another band, kill all the males, and mate with all the females, their genes would be passed on to the next generation. It is important not to have an overly rosy or idealistic view of human evolution, as this is not the way things actually work. Our diets also became less specialized, as we adapted to make full use of both hunting and gathering in getting our nutrients.
Around 250,000 years ago, Homo sapiens finally appeared, capable of making more advanced hand-axes and "reworked" stone tools, allowing it to survive in a wide variety of environments and spread across the globe.