Ancient Greece is often thought of as the cradle of Western civilization — an idea that is problematic not least because what we think of today as "Western civilization" in fact incorporates elements originating in many different times and places. Why then is ancient Greece so often singled out as its ultimate source? A determining factor is certainly the fact that we have very detailed knowledge about Greek civilization going all the way back to the 5th century B.C.E., while we lack such knowledge about other civilizations. For example, we know quite precisely how Athenian direct democracy functioned two and a half millennia ago, while we are quite ignorant of political arrangements in most of the rest of the world at that time; in particular, we know practically nothing of the political institutions among the inhabitants of northern and western Europe in pre-Roman times, though for all we know the institutions of representative democracy which are often considered a hallmark of Western civilization may in fact be more directly related to these than to anything that took place in ancient Greece. The main reason for this discrepancy in our knowledge about the past is the fact that the ancient Greeks, unlike their contemporaries almost everywhere else, left us detailed accounts of their institutions — as well as works of drama, science, mathematics, philosophy and much else — in writing, which have been preserved to this day. Without a written record, we would in principle still be able to observe the Parthenon, the Pnyx, the Greek theaters, etc., but the archeologists would be able to tell us relatively little about the uses these structures were put to; and obviously they would not be able to reconstruct for us the details of Greek philosophy, drama, science or political institutions.
The works of ancient Greek authors have been preserved not as autographs of the authors themselves but because they were copied over and over and over again by scribes, and because a few of these copies — mostly dating to the medieval period — are still in existence today in libraries where they are studied by scholars who produce editions of these works. If you know Greek, you can read these editions themselves; otherwise, you can read a translation made from one of them (also, if you know a little Greek, you can enjoy an edition with a facing translation). Either way, the indispensable link which grants us knowledge of the words formulated by an author who lived in the distant past is the extant, hand-written copy of the ancient work — the manuscript.
Etymologically, the discipline of Greek paleography (a word coined in the 18th century by Berard de Montfaucon, from the Greek elements παλαιο- "old, ancient" + γραφ- "writing, script"+ -ια, a suffix forming abstract nouns) should in principle encompass the study of all writing in Greek from the past. In fact, the study of scripts used on papyrus, on coins and medals, in inscriptions and in documents is generally left to the separate disciplines of papyrology, numismatics, epigraphy and diplomatics, while the discipline of paleography is defined as the study of bookhands employed on paper or parchment. In practice, this means that scripts from the period before the appearance of parchment books in the 4th century A.D. fall outside of the purview of our discipline, which also generally limits itself to the period before 1600 A.D., a date which is arbitrarily precise but which coincides roughly with the point when hand-written books were definitively eclipsed by printed ones.
If all copies produced by scribes were perfectly faithful ones, modern editors could simply print the text offered by any extant manuscript of an ancient author. The remaining copies would be of interest only to bibliophile collectors (and to historians of the period when the copies were made); and the ability to decipher scripts of the past would be the only skill required of the editor. Learning this skill is in fact the most basic aim of the study of paleography. However, in reality, it is almost impossible for a human to copy a long text without making at least occasional errors. In addition, since scribes knew this about themselves and about their colleagues, when they found an obscure or incomprehensible passage in the manuscript they were copying, they often attempted to correct it, which in many cases resulted in a compounded error or, even worse, produced situations where several different wordings are attested but it is unclear which (if any) of the attested wordings goes back to the original author. The upshot is that every extant manuscript of an ancient author is of interest not only to bibliophiles and to medieval historians, but also to editors of that author, who cannot work from a single manuscript source but must collect the available "variant readings" (ideally from all extant manuscripts) and decide, in each case, which one is most likely to be "original" (or conjecture a new one, if they all seem mistaken). Conscientious readers of editions of ancient authors will also want to take an interest in the manuscripts, because the decisions made by the editor can and should be questioned. These decisions are usually recorded in a critical apparatus. The information given there is normally accurate, and until recently the only realistic option for a reader has been to assume that it was; however, with more and more libraries making their manuscript collections available on line, it is now feasible, and occasionally desirable, for a reader to check the manuscripts themselves — provided, of course, that she is able to decipher them.
In passages where the manuscript tradition is divergent, how does an editor decide which reading is most likely to be original? Basing such decisions on the merits of the readings themselves alone is not very satisfactory, since in many cases their relative merits are unclear. The purpose of the discipline of paleography, as conceived by Bernard de Montfaucon (1655-1741) in his foundational work Palaeographia graeca (1708), was to give editors an objective criterion for their decisions by studying the chronological development of Greek script, thus allowing scholars to assign an approximate date (and, ideally, geographical location) to each manuscript based on the style of its script. On balance, older manuscripts will tend to have more genuine readings than more recent ones (though this is obviously not always true, since a very recent manuscript may be a very accurate copy of a very old exemplar, or may incorporate variants imported from a very old exemplar; of course it is also possible that a very old manuscript was copied very sloppily). Nowadays editors like to base their decisions on a broader understanding of how the text of their author was transmitted. They generally do this by attempting to construct a genealogy (or "stemma") representing the transmission of the text, in which the extant witnesses may be placed. This is achieved mainly by comparing the readings of the extant manuscripts (and especially by observing common errors); but obviously the ability to date the witnesses is still a fundamental prerequisite, and being able to read them in the first place is even more so.
Most people who study manuscripts are engaged in some aspect of the philological work we have just described. However, there are many other reasons why one might want to be able to read Greek manuscripts; and paleographers generally do not like to think of their field as a mere ancillary discipline serving the needs of textual critics or historians. Manuscripts are indeed vehicles for the transmission of texts, but they also have their own stories to tell and are worthy of study in their own right. They are also artifacts (and often works of art) which can tell us a great deal about to the times and places in which they were produced (e.g. educational practices; the circulation of ideas) and about the people and communities of people who wrote, bought, owned, sold and read them.
If you work through the pages of this pathway, reading the feature pages and practising your reading skills by transcribing the included manuscripts, you will be able to read most Greek manuscripts which are the object of the discipline of paleography, as defined above. You will make better progress if you are guided by a teacher, but the pathway is intended to function also as a tool for self-teaching. You may start with the first feature page, which deals with majuscule scripts.