"She does not have a cell phone."
Translation:Ella no tiene un celular.
Artsy, whether you use un or una as an article depends on the grammatical gender of the noun you want to describe. A Spanish noun has one of two genders - either masculine or feminine, and any articles and adjectives have to agree with that gender. Celular is a masculine noun, so the masculine article un is used with it. Una is the feminine article, so it would be used with a feminine noun, like "una mesa", "a table".
Ah, alright. Celular is an adjective, and adjectives get placed right behind the noun, without any preposition. Also, if you modify the noun that "someone has" with an adjective or a relative clause, it's better to include the indefinite article:
Ella no tiene un teléfono celular.