When the Anglo-Saxons first came to England from northern Germany (Saxony), they brought their language with them. It was a Germanic language, and has some fundamental similarities to German.
If Anglo-Saxon had then developed undisturbed for several centuries we might have no more trouble reading an Old English text than we do reading something written by Chaucer at the end of the fourteenth century (students can start reading Chaucer with no special linguistic instruction, though they may need the help of footnotes for the first few weeks of a course).
But political and cultural events changed the Anglo-Saxon language into the language we speak today.
The most important influence upon the language was the Norman Conquest of 1066, when William the Conquerer, a prince of Normandy (a part of France) conquered England. William made French the official language of the aristocracy and the law courts. Anglo-Norman French was an elite language, and the common people did not necessarily learn it as children, but it was the official language of the nation.
Over the next two centuries, however, Anglo-Norman French mixed with Anglo-Saxon, probably because the children of the Norman-French aristocracy were being raised by servants who spoke Anglo-Saxon among themselves. Eventually the two languages blended together, mixing the grammars and vocabularies of Anglo-Norman and Anglo-Saxon. This mixture, which was also influenced by the Latin used by the Church, became the language we recognize as Middle English, the language of Chaucer, William Langland, and the poet who wrote Sir Gawaine and the Green Knight.
But as you can see by reading even a brief passage from Chaucer, Chaucer's language is not our language. Around the year 1500, a linguistic event called "The Great Vowel Shift" occurred. No one really knows why, though there are many speculations, but within a generation or so the pronunciation of Middle English vowels was rearranged. For example, the "ee" sound in Chaucer's word "sweete" (pronounced to rhyme with "eight") became the "ee" sound in Modern English "sweet." Also the "i" in "April," which is Chaucer's time was pronounced to rhyme with Modern English "peel" became the short "i" sound in Modern English "April." All the vowels were rearranged in a complex pattern that you can learn if you take a linguistics class.
Once this vowel shift is complete, we have Early Modern English and, soon after, Modern English. Thus while Chaucer takes some getting used to, students can successfully read the writings of Shakespeare with no formal instruction in language; our language, for all the new words added and changes in manners and style, is essentially the same as Shakespeare's. We could have understood Shakespeare, and he could have understand us, but he could not have understood Ælfric, even though approximately the same amount of time separates Ælfric from Shakespeare as separates Shakespeare from us.
But despite the differences between Old English and Modern English, the language retains a fundamental kinship to our own. Thus students can expect to find learning Old English to be somewhat easier than learning a new "foreign" language such as Spanish or French. A semester's worth of hard work should be enough to give a student the ability to translate Old English poetry and prose. The key to success in this endeavor is to lay a solid foundation of grammatical understanding. While at first it may seem easy to "get the general idea" of a passage, if you take the time to figure out exactly how each word is working in a sentence, you will find that the more complicated Old English sentences that we meet later in the semester will be less difficult to translate than they otherwise might be.
It is also important for students to realize that this short work is no permanent substitute for a real grammar book, such as Mitchell and Robinson's A Guide to Old English. King Alfred's Grammar skips over exceptions to rules, complications of syntax and some subtleties of Old English grammar. The time in a semester is so short, and the number of things worth learning so many that we felt justified in this simplification. So King Alfred's Grammar makes no pretense to being a complete analysis of Old English grammar. Its sole purpose is to get students translating great literature as quickly as humanly possible and thus, hopefully, lead to further study in Old English literature and culture.