Hey /r/greatprophet69
It is too late for a large, well-written, and well organized essay so I will offer you a few answers that I am reporting from Diarmaid MacCulloch's Reformation:A History.
The phenomenon that led historians from the early Reformations/Renaissance time period to pursue the world of old documents/writings from the Greeks and Romans was called "Humanism". Not to be confused with the modern version of that word that means a rejection of claims from revealed religion (Christianity, etc), the "Humanism" as it was referred to back in the day was a sort of looking to the past (Greeks/Romans) in order to better society in their time. Basically, it was the realization that there was more to life than the Middle Age Scholasticism (MacCulloch 76-80).
ANYWAY, one of the big aspects of the Renaissance was a greater printing capability which made reproducing texts easier. This in turn increased literacy which lead to a more intense search for ancient manuscripts. Greek manuscripts turned up this way as they were neglected (MacCulloch 78).
Another big aspect that impacted the spread of Roman/Greek manuscripts was interactions with the Arabs. During the Ottoman conquests the manuscripts were brought west by scholars bringing Greek culture. Also, entrepreneurs would also deal in such documents. For instance, a dude named Giovanni Aurispa brought back some of the famous greeks from Constantinople thirty years before Constantinople was sacked (MacCulloch 78).
EDIT: Grammar
If you're referring to the works of bigwigs like Cicero, Julius Caesar, and Plato, the answer is generally simple: they were never lost. Cicero, for instance, influenced many important figures of Late Antiquity (St. Augustine and Jerome in the 5th century) and Isidore of Sevilla is known for preserving a number of Latin texts that would be used by later medieval scholars. When individual letters or more obscure authors went out of vogue, they could still be found at one monastery or another; Rennaissance scholars like Petrarch compiled and publicized these.
There do still remain many authors whose works are fragmentary or completely lost. Epicurus, the namesake of Epicureanism, is known through references and quotes in later authors like Lucretius, though none of his original work survived/has been found.