Learn Spanish (Latin America): La prima del profesor necesita una mesa nueva.

In Spanish, there is no apostrophe 's' for possession. Instead, you describe the relationship by saying 'the cousin of the teacher' using the word de (of). When de is followed directly by the masculine word el (the), they combine into the contraction del.

How do we know from the sentence that the cousin is female, but the teacher is male?

Spanish uses masculine and feminine forms for people. La prima uses the feminine la and ends in -a, meaning she is a female cousin. The teacher is el profesor, which is masculine. If the teacher were female, it would be la profesora, and the sentence would say de la profesora instead of del profesor.

Why is it una mesa nueva instead of una nueva mesa?

In English, descriptive words (adjectives) usually come before the noun they describe (like 'a new table'). In Spanish, it is usually the other way around: the noun comes first, followed by the adjective. So, you literally say 'a table new' (una mesa nueva).

Why does the verb end in -a (necesita)?