The more familiar European languages use a word preceding the
noun. In English it is entirely uninflected; in French, Italian, and Spanish it is
inflected for
gender and number; in German and Greek it is inflected for gender, number, and
case, as it was in
Old English and
Old Norse.
In Scandinavian languages it is a suffix. In Old Norse it could be either a preceding word or a suffix. For example, 'the king' was hinn konungr or konungrinn, and 'the ship' was hit skip or skipit. Modern Icelandic uses only the suffixal form: konungurinn, skipið. In modern Swedish a different deictic, den, is used as the prefixed form if one is wanted in addition to the suffix -en.
Slavonic languages do not have definite articles, except Bulgarian, which uses a suffix. Strangely enough, so does Romanian use a suffix even though no other Romance language does, and so does Albanian. None of these three are closely related, so it must be an areal thing propagated from one into its neighbours. (See Sprachbund.)
Welsh has an uninflected article y before a consonant, yr before a vowel, but in the feminine singular this causes soft mutation in the following word. So cath 'cat', y gath 'the cat'. The Irish article retains some inflection and likewise causes mutation.
Outside the Indo-European family, definite articles as such are perhaps not so often encountered, though most languages have a way of marking definiteness.
In Arabic the article is al-, in Hebrew it is ha-. The Arabic article assimilates to some following consonants, and the Hebrew one doubles most following consonants (and may itself slightly change shape with the others).
In Turkish there is no article as such, but the accusative case is only used if the direct object is definite, otherwise it remains is the nominative.
In Swahili a definite direct object is marked with a cross-reference pronoun inside the verb, but an indefinite object is not. This and Turkish illustrate a general point, that objects are more likely to be specially marked if definite.