How did the French Revolution end up with an Emperor Napoleon gobbling up the world as his fiefdom?

The 10 years following the revolution saw the country in chaos, as people were quick to denounce anyone they disliked and have them sent to the guillotine. Napoleon was seen as someone able to bring back order and more, conquests.

For the record, while France was just annexing neighboring small territories, it was the declaration of war by UK that escalated things to the proportion where Napoleon felt he really had to do battle and, consequently, occupy land.

And since the 3rd coalition included UK, the Austrian Empire, and the Russian Empire, it pretty much involved going East pretty far to win that one.