Learn Spanish (Latin America): El jarrón blanco está al lado de la ventana.

It literally translates to "at the side of." The word lado means "side," and al is the mandatory contraction of a + el (to/at the). So, al lado means "at the side," and de (of) connects it to the window.

Do I always have to use de after al lado?

You need de when you are specifically naming the thing it is next to. Since we say what the vase is next to (la ventana), we must use de. If someone asked where the vase is and you just wanted to answer "It's on the side" or "It's next to it," you would just say Está al lado and drop the de.

Why doesn't al lado change to feminine to match la ventana?

Because al lado de is a fixed phrase built around the masculine noun el lado (the side). Even though la ventana is feminine, the phrase "at the side of" always stays exactly the same. It never changes to match the objects around it.

Why do we use está instead of es here?