How did the world get populated?

Answer 1

The short answer: sex.

The long (but still short) answer: I'm assuming you're referring to humans. 3.5-3.8 billions years ago was the last universal common ancestor, the species that all current species came from. A few billion years of evolution later, Homo sapiens sapiens, anatomically modern humans appear. From about 40,000 years ago until about 10,000 years ago humans colonized the planet. After the agricultural revolution ~10,500 years ago, humans were able to live sedentary lives and this led to population increase. Over the past 200 years, scientific advances allowed for much greater survival, and the world population has increased from about 2 billion to nearly 7 billion.