how did the roman empire fall?

here's your answer

http://www.ushistory.org/civ/6f.asp

The invading army reached the outskirts of Rome, which had been left totally undefended. In 410 C.E., the Visigoths, led by Alaric, breached the walls of Rome and sacked the capital of the Roman Empire.

The Visigoths looted, burned, and pillaged their way through the city, leaving a wake of destruction wherever they went. The plundering continued for three days. For the first time in nearly a millennium, the city of Rome was in the hands of someone other than the Romans. This was the first time that the city of Rome was sacked, but by no means the last