The direct reason for Rome falling was because of an attack from barbarians in 476CE, with Odoacer exiling the last Roman emperor, Odoacer.
The barbarians were able to get in because many of the "barbarians" were already in the empire as Germanic soldiers, who were most loyal to money, not Rome.
Another reason for the fall of Rome was the empire's over-reliance on slaves. They were used for building and agriculture. When slaves ran out, Rome had to pay for all of the workers doing jobs from then on.
What? Can't hear you!
Another cause for Rome's fall was the empire's economical problems. The military took up 30% of the empire's budget, which became unsustainable.
In addition, in around 300CE, the east of the Roman empire had become the Byzantine Empire, with a very urbanised Constantinople, which caused the west side, the one with Rome, to become more poor.
Also, the fall of Rome was partially because of the empire's fixation on expansion. The further the empire spread from Rome, the less power it had on that land.