Overview of Nouns
Each noun in Greek has three grammatical categories: Case, Number, and Gender. The noun can change in case and number (this is called inflection). The gender of the noun is fixed.
Greek nouns can change across four main cases: Nominative, Genitive, Dative, and Accusative. There is a fifth case -- Vocative, which is used much more rarely and which we won't discuss too much.
Greek nouns can change in number between Singular and Plural, just like in English. Before there was also a Dual number, however, it does not exist in Koine Greek.
There are three grammatical genders in Greek: Masculine, Feminine and Neuter. Each word has a fixed grammatical gender. In the case of the nouns designating people, grammatical gender usually corresponds to actual gender. In any other case, the gender has to be memorized.
The dictionary form of a noun consists of the Nominative Singular form, the Genitive Singular ending and the Nominative Singular article. The article specifies the gender of the noun. All this information is usually enough to specify the declension.