Old english vocabulary

An example: The following couple of lines from Ælfric’s De temporibus anni:
‘Ðunor cymð of hætan & of wætan. Seo lyft tyhð þone wætan to hire neoðan & ða hætan ufan.’
may be translated word-for-word as:
Thunder comes from heat and from moisture. The air draws the moisture to it from below and the heat from above.
To pick out a very few grammatical features:
The nouns hæte, ‘heat’, and wæta, ‘moisture’, both have the inflection –an in the first sentence, because both are in the dative case, governed by the preposition of ‘from’.
In the second sentence they both again have the inflection –an, but this time they are in the accusative case, as the direct objects of tyhð ‘draws’.
The forms of the definite article agree with these nouns, but you will note that they are different in each instance, þone wætan ‘the moisture’ (direct object), but ða hætan ‘the heat’ (also direct object). The difference arises because wæta ‘moisture’ is masculine but hæte ‘heat’ is feminine, and the article (like other adjectives) agrees in gender as well as case.
For another example of gender agreement, look at the pronoun hire (i.e. the antecedent of modern English her) referring to seo lyft (feminine) ‘the air’.
In vocabulary, Old English is much more homogeneous than later stages in the history of English. Some borrowings from Latin date back to before the coming of the Anglo-Saxons to Britain (i.e. they were borrowed on the continent), while many others date from the period of the conversion to Christianity and later. However, words borrowed from Latin or from other languages make up only a tiny percentage of the vocabulary of Old English, and the major influx of words from French and from Latin belongs to the Middle English period and later. (There are also numerous loan translations and semantic loans from Latin in Old English, reflecting the influence of Latin on the language of religion and learning.)
Some Old English words of Latin origin that have survived into modern English include belt, butter, chalk, chest, cup, fan, fork, mile, minster, mint, monk, pepper, school, sock, strop, wine.
Some borrowing from early Scandinavian is attested in later Old English, but again the major impact of contact with Scandinavian settlers becomes evident only in Middle English.
There is also a great deal of continuity between Old English and later stages in the history of the language. A great deal of the core vocabulary of modern English goes back to Old English, including most of the words most frequently used today.
For a very few examples see I pron. and n.², one adj., n., and pron., and conj.¹, adv., and n., man n.¹ (and int.), woman n.
For further information on which Old English words are included in the OED, and on how Old English material is dated in the dictionary, see Old English in the OED by Anthony Esposito.
Some letters from the Old English alphabet which modern English has lost:

• 
  þ, ð both represent the same sounds as modern th, as e.g. in thin or then;
  
• 
  æ and a represent distinct sounds in Old English, formed with the tongue respectively at the front and back of the mouth.
  

The pronunciation of e.g. trap or man in many modern varieties of English comes close to Old English æ, whereas Old English a was more like the sound in modern German Mann ‘man’ or Spanish mano ‘hand’ (like the sound in modern English father, but shorter).
The beginning of Old English …
It is very difficult to say when Old English began, because this pushes us back beyond the date of our earliest records for either Old English or any of its closest relatives (with the exception of very occasional inscriptions and the evidence of words and names occurring in Latin or in other languages). Everyone agrees in calling the language of our earliest extensive sources found in contemporary copies ‘Old English’: these are Latin-English glossaries from around the year 700. (Some other material was certainly composed before 700, but survives only in later copies.) By this time Old English was already very distinct from its Germanic sister languages (see below) as a result of many sound changes (i.e. changes in how certain sounds were pronounced, chiefly when they occurred near to certain other sounds) and other linguistic developments. In fact, most of the most important changes which we can trace through our surviving Old English documents had already happened before this time. Some of them were very probably well in progress or even complete before the time of the settlement in England.
Some Latin-English glosses from one of our earliest sources (the Épinal Glossary):

• 
  anser goos (i.e. ‘goose’)
  
• 
  lepus, leporis hara (i.e. ‘hare’)
  
• 
  nimbus storm (i.e. ‘storm’)
  
• 
  olor suan (i.e. ‘swan’)
  

Some scholars distinguish the undocumented period before our earliest texts as ‘pre-Old English’, while others are happy just to use the name ‘Old English’ for this period as well as for the documented period. In practice, the dividing line is hazy. Most of our documentary evidence for Old English comes from much later (late ninth century and onwards), and even in the later period there is much that we do not know. In the earlier part of the documented period, the gaps and uncertainties mean that we often know just as little about a certain topic as we do for the preceding undocumented period.
If we trace its history back further, Old English belongs to the West Germanic branch of the Germanic languages, along with Old Frisian, Old Saxon, Old High German, and the various dialects which later gave rise to Old Dutch. The major early representatives of the North Germanic branch are Old Icelandic, Old Norwegian, Old Swedish, and Old Danish (although the earliest extensive remains for all of these are much later than the earliest Old English documents), while the only representative of the East Germanic branch for which extensive remains survive is Gothic. Ultimately, all of these branches diverged from a single hypothetical ancestor, (proto-)Germanic, which itself constitutes a branch of the larger Indo-European language family. Other branches of Indo-European include Celtic, Italic (including Latin and hence the Romance languages), Greek, Indo-Iranian (including Sanskrit and Persian), Baltic, and Slavonic (these last two being regarded by many as a single branch, Balto-Slavonic).
In fact, very many details of the pre-historic relationships between Old English and the other Germanic languages are much debated and very controversial, which greatly complicates any attempt to say when ‘Old English’ began.
The end of Old English
The conventional dividing date of approximately 1150 between Old English and Middle English reflects (very roughly) the period when these changes in grammar and vocabulary begin to become noticeable in most of the surviving texts (which are not very numerous from this transitional period). In what is often called ‘transitional English’ the number of distinct inflections becomes fewer, and word order takes on an increasing functional load. At the same time borrowings from French and (especially in northern and eastern texts) from early Scandinavian become more frequent. All of these processes were extremely gradual, and did not happen at the same rate in all places. Therefore any dividing date is very arbitrary, and can only reflect these developments very approximately.
Old English dialects
The surviving Old English documents are traditionally attributed to four different major dialects: Kentish (in the south-east), West Saxon (in the south-west), Mercian (in the midland territories of Mercia), and Northumbrian (in the north); because of various similarities they show, Mercian and Northumbrian are often grouped together as Anglian. This division is largely based on linguistic differences shown by various of the major early sources, although many of the details are highly controversial, and some scholars are very critical of the traditional association of these linguistic differences (however approximately) with the boundaries of various politically defined areas (which are themselves only poorly understood), and today many of the details of where each variety was centred geographically are subject to debate. For political and cultural reasons, manuscripts written in the West Saxon dialect hugely predominate among our later records (although much of the verse is something of a special case), reflecting the widespread adoption of a form of West Saxon as a written language in the later Old English period.