I understand that traditionally, the fall of the Roman Empire was after the death of the last emperor. What I'm curious about is the time period after this; obviously the entire empire didn't just disappear off the face of the Earth so what happened? Any readings on this time would be greatly appreciated. I'd love to learn more
Romulus Augustulus was proclaimed emperor as a child by his father Orestes, who used his son as a figurehead. The boy emperor was deposed by Odovacer (allegedly Odovacer was the son of a Hunnic ambassador, Edeko, during the reign of Attila). However Romulus Augustulus didn't die when he was deposed but was allowed to live out his days in retirement in Naples, apparently as late as 507 AD.
In terms of what happened next; it's a series of invasions, sackings of Rome and overthrows until Justinian's Gothic War in the 530s, the rise of the Lombards and then Charlemagne in 800.
There's a lot of answers already in the FAQ that might be able to answer specific questions on why the Empire fell along with the society, economy, religion, invasions and legacy in the post-Rome era.
Odoacer had deposed Romulus Augustulus when he lost the army's favor. At this point in time years of civil wars had brought a long succession of army-backed strongmen to power, many of whom had mixed heritage (just like most soldiers); Romulus Augustulus, the last emperor, was himself was a puppet of his father Orestes, who had married into a Roman family but himself was not an ethnic Roman (and to be pedantic, the Eastern Emperor never even recognized Augustulus, which allowed Julius Nepos, the pervious emperor, to rule in semi-autonomy in Dalmatia claiming all the while to be Emperor of the West. This can give you an idea as to how chaotic things had been getting in Italy at this point). Odoacer, unlike his predecessors, openly admitted that although his "martial law" allowed him to rule Italy, he was powerless beyond the alps, and never called himself Emperor, rather, he sent the imperial paraphernalia to Constantinople and asked to be recognized as "Consul", keeping all of the functions of the Roman administration in Italy intact (indeed, Flavius Odoacer was so Romanized historians aren't even sure which "Barbarian" ethnic group he belonged to). He initially played lip service to the pervious emperor Julius Nepos, who all the while had been hanging out in Dalmatia since Romolus Augustulus deposed him. Odoacer even minted coinage in Julius Nepos' name, but this didn't stop him from from (probably, there's only circumstantial evidence) getting involved in the plot whereby he was eventually murdered. Regardless, after the murder of Julius Nepos, Odoacer asked to be given the title of Patrician by the Eastern Emperor, and be recognized as the ruler of Italy under the wing of a single Roman Emperor in Costantinople.