How did Rome fall, and who brought about its demise?

Rome fell due to a variety of circumstances, which I will break down here.

Political and Military Instability - by the 5th century, Roman emperors in the west had long been figureheads and puppets. Civil war was constant, with different portions of the army backing several claimants to the throne. These claimants had little power in reality. Barbarian Generals, such as Ricimer, often pulled the strings of succession. The army and political leaderships were mostly barbarian. Long gone were the days of the Romans serving in the roman army. Hired barbarian mercenaries were often the core of a Roman military unit now, bringing with them their own tactics, style, equipment and (compared to the legions of the republic and early empire) lack of organization and training. Soldiers were often no longer loyal to Rome or the empire, but to their own commander. This had happened often in the past in the military, however, most truly Roman generals respected the empire and were loyal to the emperor. the now barbarian army was led by barbarian commanders, many of whom had never even seen Rome. Rome was sacked in 410 for the first time in over 700 years and would be sacked again in 455 and finally in 476. That would mean that someone who was born in 400 could likely see 3 sackings of Rome in his or her lifetime - that would be laughable to even speak of the city being sacked once in the time of Augustus.

Financial Crisis - The Roman economy had struggled since the crisis of the 3rd century and the ensuing 50 year civil war(s). debasement of currency had been a problem for a long time. The denarius, the silver coin of the Roman republic and empire, had been pure silver under Augustus. By the mid 3rd century, it contained roughly 5% silver. In Roman times, the quick fix was simply to make more money, and this was achieved by gradually using less and less silver. That's all well and good, but if you flood the market with money, it loses its value. This is a problem we still see today with inflation and deflation of currency. The division of the empire also significantly hurt the western half, as most of the empire's wealth, and it's grain (Egypt is often referred to as "Rome's Breadbasket"), resided in the east. Since the time of the Tetrarchy (begun in 285), Emperors had invested heavily in the Eastern half of the empire. The last great public work in Rome (the Basilica of Maxentius - or Constantine) was completed in 312. The east was where the money was, in laymen's terms.

New Capitals - This goes along with the division of the empire, I mentioned. The establishment of Constantinople as the "New Rome" was detrimental to the west. Constantine encouraged senators and wealthy Romans to relocate to his new city, further pulling power away from a city (Rome) that was already suffering. Rome had long since lost its place as the political heart of the empire to cities such as Trier, Mediolanum or Ravenna. The city still served as the spiritual heart and home of the Romans, however, politically it became of lesser importance.

Internal Issues, leading to Border Issues - The internal instability covered so far led to instability on the borders of the empire. To account for constant civil warring and political unrest, troops were gradually pulled away from Britania and Gaul/Germania to protect Italy, in turn leading to revolts and a general free-for-all in those regions amongst competing tribes. A similar situation occurred in Spain, where the Vandals took control and then moved into North Africa, weakening Rome's grip on the Mediterranean (Long referred by the Romans as Mare Nostrum, meaning "Our Sea"). Many Barbarians moving into these areas simply wanted to be a part of the Empire at first. Odoacer, who sacked Rome for the final time in 476, simply wanted to be a part of the Roman system. Many of the groups desired to reside in the frontier areas. However, after mistreatment from the empire, these groups knew they could not peacefully get what they desired. By the time they truly "invaded", the cracks in the Empire were already there. They simply put enough weight on these cracks for the dam to break, so to speak.

These are a few of the main factors, but if you want to read more there is certainly a wealth of information on this particular topic. See the sources for some I would suggest.

The History of the Decline and Fall of the Roman Empire by Gibbon

The Ruin of the Roman Empire by O'Donnell

The Fall of the Roman Empire: A New History of Rome and the Barbarians by Heather