Old English/Articles

Articles are actually just a special kind of adjective. They are adjectives which show the definiteness of the noun being referred to. In Modern English, we have several articles:
 * The definite article (in Modern English "the") shows that a substantive is a particular noun that the listener should recognize
 * The indefinite (in Modern English "a","an", or "some" for plural) shows that a substantive is not a specific noun that the listener should recognize
 * The negative article (in Modern English "no") shows that there is none of the substantive

In Old English, their definite article was also used as a demonstrative adjective and as a demonstrative pronoun, equivalent to Modern English "that" or "that one". You can see it on the pronouns page here.

Definite articles and demonstratives
Old English had two main determiners: se, which could function as both 'the' or 'that', and þes for 'this'.

Modern English 'that' descends from the neuter nominative/accusative form, and 'the' from the masculine nominative form, with 's' replaced analogously by the 'th' of the other forms.

Also, in Old English they generally had no indefinite article (although occasionally their word for "one" - ān could be translated into Modern English as "a" or "an"). So in speaking Old English, a noun with no article at all would often be the equivalent to a noun with an indefinite article in Modern English, for example hūs - "a house", and dēor - "an animal".

There were several words that could be used to translate the negative article "no" in Old English:
 * nān - "none" (used in West Saxon)
 * nǣniġ - "none" (used in Anglian dialects)

They both followed the normal strong adjectival declension (for which see here) and agreed with the nouns they modified.

Articles were declined in agreement with whatever noun they modified, just like adjectives. For example, to say "the people", you would have to use the plural form of both "person" (mann) and "the" (sē): þā menn. To say "this woman's house", you would need to use genitive of "woman" (ƿīf) and the neuter singular definitive article: þæs ƿīfes hūs.