Learn French: Je travaille à la bibliothèque le week-end.

In French, the preposition à (at/to) only contracts with the masculine article le (becoming au) or the plural article les (becoming aux). Since bibliothèque is a feminine noun, it uses la. The words à and la never contract, so they stay separate as à la.

The translation says "on weekends," but the French sentence just says le week-end (singular). Why is that?

In French, using the singular definite article (le) before a day of the week or week-end tells us that the action is a recurring habit. So, le week-end translates beautifully to "on weekends" or "every weekend."

Why isn't there a word for "on" before le week-end?

French doesn't use a preposition like "on" or "at" for days of the week or weekends. You simply use the article le directly before the noun.

I always confuse bibliothèque with the word for bookstore. How do I tell them apart?

This is a classic "false friend"! La bibliothèque means the library (where you borrow books), while la librairie means the bookstore (where you buy them).