Appendo il quadro sopra il divano.

Appendo is the first person singular (io) present indicative of the verb appendere, which means “to hang.”
Infinitive: appendere
Conjugation in the present tense:

• io appendo
• tu appendi
• lui/lei appende
  …
  Knowing this lets you say “I hang,” “you hang,” etc., in Italian.

In Italian, singular countable nouns typically require an article—definite (il, la) or indefinite (un, una).

• il quadro = “the painting”
• il divano = “the couch/sofa”
  You can’t drop the article the way you sometimes do in English (“I hang painting above couch” is ungrammatical in Italian).

Both sopra and su can mean “on” or “above,” but they carry a slight nuance:

• su is more general (“on,” “onto,” “upon”).
• sopra often emphasizes “directly above” or “over” something, not necessarily touching it.
  In our sentence, sopra il divano implies the painting hangs on the wall just above the couch, not resting on it.

Yes, su + il contracts to sul, so sul divano means “on the couch” (touching it).

• Lo metto sul divano = “I put it on the couch.”
  But for a painting you don’t hang it on the couch itself—you hang it above on the wall—so you use sopra il divano.

Italian word order for a neutral statement is Subject–Verb–Object–Adverbial/Prepositional Phrase.

• Subject (implied io)
• Verb appendo
• Object il quadro
• Locative phrase sopra il divano
  You can front a prepositional phrase for emphasis (“Sopra il divano appendo il quadro”), but it sounds marked or poetic rather than everyday speech.

The masculine singular direct object pronoun is lo. With a finite verb, it precedes the verb:

• Lo appendo sopra il divano. (“I hang it above the couch.”)
  In a compound tense you’d say:
• L’ho appeso sopra il divano.
  Here l’ is the apocoped form of lo before ho.