Dopo cena montiamo il tavolo, ma domani dobbiamo ancora smontare la vecchia libreria.

In Italian, meals are often used without an article in time expressions:

• dopo cena = after dinner
• prima di colazione = before breakfast
• a pranzo = at lunch / for lunch

So dopo cena is the natural general expression meaning after dinner.

Dopo la cena is possible, but it sounds more specific, like after the dinner or after that dinner.

Italian very often uses the present tense to talk about the future when the time is already clear from context.

Here, dopo cena makes the timing clear, so:

• Dopo cena montiamo il tavolo
  literally looks like After dinner we assemble the table,
  but it means After dinner we’ll assemble the table.

This is extremely common in everyday Italian.

Here montare means to assemble, to put together, or to set up something made of parts, such as furniture.

So montiamo il tavolo means:

• we assemble the table
• we put the table together

It is often used for furniture, equipment, shelves, and similar objects.

No. That is an important difference.

• montare il tavolo = assemble the table physically
• apparecchiare la tavola = set the table for a meal

So in this sentence, they are not putting plates and cutlery on the table. They are building or assembling the table itself.

Yes. Smontare is the opposite of montare.

• montare = to assemble / put together
• smontare = to take apart / disassemble

The prefix s- often gives the idea of undoing or reversing an action.

So:

• montare una libreria = assemble a bookcase
• smontare una libreria = disassemble a bookcase

Because dovere works like a modal verb, similar to must / have to in English.

• dobbiamo = we must / we have to
• smontare = to disassemble

After dovere, the next verb stays in the infinitive:

• dobbiamo partire = we have to leave
• devo studiare = I have to study
• dobbiamo smontare la vecchia libreria = we have to disassemble the old bookcase

Here ancora means still or yet.

• dobbiamo ancora smontare la vecchia libreria
  = we still have to disassemble the old bookcase
  = we haven’t done it yet

So ancora shows that this task remains unfinished.

That position is very natural in Italian.

• dobbiamo ancora smontare la vecchia libreria

Here ancora modifies the whole action: we still have to disassemble.

You may also hear slightly different word orders in Italian depending on emphasis, but this one is standard and very common.

This is a classic false friend.

In Italian:

• libreria = bookcase / bookshelf
• libreria can also sometimes mean a bookstore in certain contexts, but the more common word for bookstore is liberia? No — be careful: the correct Italian word is libreria for bookstore in many contexts, but in this sentence, because it is something you can smontare, it clearly means bookcase / shelving unit.

For a learner, the key point is: in sentences about furniture, libreria usually means bookcase.

Italian uses definite articles much more often than English.

So where English might say:

• assemble the table
• disassemble the old bookcase

Italian naturally says:

• il tavolo
• la vecchia libreria

Even when English might sometimes omit an article in a broader context, Italian often keeps it.

In Italian, many adjectives can come after or before the noun, but the position can affect style or nuance.

• la vecchia libreria = the old bookcase
• la libreria vecchia is less natural here

With common descriptive adjectives like vecchio, putting the adjective before the noun is very common and often sounds more natural in everyday speech.

Also, vecchia libreria can simply mean old bookcase, but depending on context it may also suggest the previous/older bookcase, not necessarily just an aged one.

Because domani is setting the time for the second clause:

• ma domani dobbiamo ancora smontare la vecchia libreria

Italian word order is flexible, and placing domani early makes the time reference clear right away: but tomorrow...

That is very natural. You could move time expressions around in other sentences, but this position is common and straightforward.

Yes, it could, but the present tense sounds very natural here.

For example:

• Dopo cena monteremo il tavolo, ma domani dovremo ancora smontare la vecchia libreria.

This is grammatical, but often a bit more formal or marked in everyday conversation.

In normal spoken Italian, the present tense is usually preferred when words like dopo cena and domani already make the future meaning obvious.