PREFACE
The difficulty with writing about the history of the Slovak language is mainly the lack of information from various stages of its developement. Since it's standardisation process began relatively lately, and the later was completed, studying the medieval history thereof is, at best, challenging.

CLASSIFICATION
Slovak language belongs to the Balto-Slavic, more specifically Slavic branch of Indo-European languages, and is thus related to Germanic, Italic, Anatolian, Tocharian, Indo-Iranian and other branches of the same family.

SLAVIC PROTO-LANGUAGE AND URHEIMAT
Unlike Germanic languages, the issue of the urheimat of Slavonic languages is still a subject of debate, as well as its classification in the proposed Balto-Slavic connection. Nonetheless, the historical and linguistic mainstream generally agrees that the urheimat was somewhere in the eastern Europe, surrounded by rivers Vistula, Bug, Dneper and Don and the Proto-Slavic language itself was spoken since the early 1st millennium B.C. Just like Germanic and every other branch, Slavic language underwent several consonantal and vowel shifts that gradually distinguished them from their Indo-European cousins. Since we all are native speakers of a Slavic language - Slovak - I am going to mention one consonantal shift, the result whereof you might find interesting.

PIE g became Slavic ž, dz, or z. Examples:
PIE qwén became žena (the Germanic word for woman/wife is kwoeniz, whence English queen, Swedish kvinna or Gothic qino and other)
PGmc kunningaz became kunedzi, later kniez, modern Slovak knieža (whence also English king, Swedish kung, Norwegian kuning, Frankish cuning, Anglo-Saxon cyning and other)
PIE ghol became zoloto...OCS/Slovak/Czech zlato (PGmc got gulth, whence English gold)

DISPERSAL INTO FOUR BRANCHES
From their urheimat Slavs dispersed into all directions and gradually their languages differed form one another. This is when we start to speak of four different branches of Slavonic languages: southern, western, eastern and the hypothetical northern (Old Novgorod dialect pertained a lot of archaic elements and is thus believed to have formed a separate northern branch, but is extinct today). This happened around 500-700A.D. Since it is an essay about Slovak language, I shall concentrate on the western and southern branches only.

SOUTHERN SLAVIC LANGUAGES
The greatest importance of this branch definitely belongs to the Old Bulgarian language (also known as Old Church Slavonic). The language was codified by Byzantine Greek brothers Constantine and Methodius, who also indited the script called Glagolics (a modification of the Greek script), which came into use mostly in formal and church matters.

WESTERN SLAVIC LANGUAGES
The western dialect of Proto-Slavic later developed into further dialects and much later into independent languages: Czech, Slovak, Sorbian and Lechitic (whence Polish, Pomeranian, Silesian and Polabian).
In 863 the aforementioned Greek brothers were invited (by knyaz Rastislav) to the Great Moravia to spread the new liturgical script, so that Moravians would become independent of the German influence.
The successor of Rastislav, knyaz Svatopluk, however, expelled the educatees of the two Greeks and one of them (Clementis) left for Bulgaria, where he futher modified the Glagolic script into Cyrilics.

THE BIRTH OF SLOVAK LANGUAGE
Firstly, I feel the need to clarify a certain issue: Slovak is not descentant of Old Church Slavonic - if your Slovak language teacher claims so, do not believe her - she probably is confused/uneducated about the developement of the early Slavic languages. Slovak only took some influence from Old Church Slavonic.