Learn French: Est-ce que tu vas à la piscine avec moi ? - Are you going to the swimming pool with me?

Vas is the "you" (tu) form of the irregular verb aller (to go). In the present tense, it goes: je vais (I go), tu vas (you go), and il/elle va (he/she goes). Since you are addressing "you" informally here, you must use vas.

What does Est-ce que mean at the start of the sentence?

Literally, it means "Is it that". In French, putting Est-ce que at the beginning of a normal statement is the most common way to turn it into a yes-or-no question. Tu vas means "You are going", so Est-ce que tu vas... ? means "Are you going...?".

Why do we say à la piscine?

The verb aller is usually followed by the preposition à (to). Because piscine (swimming pool) is a feminine noun, it uses the feminine word for "the", which is la. If you were going to a masculine place, like the park (le parc), à and le would combine into the single word au.

Why is it avec moi and not "avec je" or "avec me"?