Indefinite articles are used when referring to a nonspecific noun (or a category). "Ein Buch," for example, rather than the definite "das Buch". Indefinite articles can change depending upon the gender of the noun and upon case. "Ein Buch" in the nominative becomes "einem Buch" in the dative.
In the sentences below consider the gender and case of the noun, and fill in the blank with the correct form of the indefinite article.