Learn Italian: Il quadro è sopra il divano. - The painting is above the sofa.

While both translate to location words, su usually implies direct contact, like sitting right on the cushions (sul divano). Sopra means "above" or "over," which is perfect for a painting hanging on the wall higher up. Sopra can sometimes mean "on top of" with direct contact, but su cannot mean "above" without contact.

Do I need to say sopra a or just sopra?

You can use just sopra followed directly by the article and noun, as shown here with sopra il divano. In conversational Italian, you will often hear people add the preposition a, saying sopra al divano. Both are accepted and understood, but dropping the a is considered the standard form for written Italian.

Can quadro be used for any type of picture?

Quadro specifically refers to a framed picture or painting, typically one that hangs on a wall (the word comes from the shape of a "square"). For a casual photograph, you would use foto, and if you want to emphasize the painted artwork itself rather than the framed object, you might use dipinto.