The indefinite articles correspond to English "a/an" and "some": un before a masculine singular noun (un livre, a book), une before a feminine singular noun (une pomme, an apple), and des before any plural noun (des livres, some books; des pommes, some apples).
Unlike English, French rarely drops the article before a plural noun — where English can say "I eat apples" with no article at all, French requires je mange des pommes. In a negative sentence, however, un, une, and des all collapse to a bare de (or d' before a vowel): j'ai un chat becomes je n'ai pas de chat, not je n'ai pas un chat.