Du laboristinoj venis frue por ripari la tegmenton kaj savi la malsekajn librojn en la ĉambro supre.

Because it is built from several Esperanto pieces:

• labor- = work
• -ist- = a person who does an activity or has an occupation
• -in- = female
• -o = noun ending
• -j = plural

So laboristinoj means female workers or working women.
The singular would be laboristino.

Because du is just the number two, and the noun only needs the plural ending -j unless it is also a direct object.

Here, laboristinoj is the subject of the sentence, so it is plural but not accusative:

• du laboristinoj = two female workers

If it were a direct object, it would take -n as well:

• Mi vidis du laboristinojn. = I saw two female workers.

Venis is the past tense of veni = to come.

Esperanto verb endings are very regular:

• -i = infinitive → veni = to come
• -as = present → venas
• -is = past → venis
• -os = future → venos

So Du laboristinoj venis means Two female workers came.

Frue means early. The ending -e marks an adverb in Esperanto.

Compare:

• frua = early, early-related (adjective)
• frue = early (adverb)

Since it describes how they came, Esperanto uses the adverb:

• venis frue = came early

Because por means for / in order to, and after por Esperanto normally uses the infinitive.

So:

• por ripari = in order to repair
• por savi = in order to save

This works much like English to repair and to save after in order to.

Because it is the direct object of ripari.

They came early to repair what?
Answer: la tegmenton = the roof

In Esperanto, the direct object takes -n:

• ripari la tegmenton = to repair the roof

The basic noun is tegmento.
With the accusative ending, it becomes tegmenton.

Because adjectives in Esperanto agree with the nouns they describe in both number and accusative marking.

Here:

• libroj = books
• librojn = books as a direct object
• malsekaj = wet (plural)
• malsekajn = wet (plural direct object)

So both words show:

• -j for plural
• -n for accusative

This agreement is a central Esperanto rule:

• la malsekaj libroj = the wet books
• la malsekajn librojn = the wet books as object

Because here en la ĉambro supre expresses location, not motion toward something.

• en la ĉambro = in the room

When en shows where something is, no accusative is needed.
If it showed motion into a place, Esperanto often uses -n:

• Li estas en la ĉambro. = He is in the room.
• Li iris en la ĉambron. = He went into the room.

In your sentence, the books are located in the room upstairs, so ĉambro stays without -n.

Supre means above / upstairs / up above, depending on context.

In en la ĉambro supre, it means something like:

• in the room upstairs
• in the room above

It is an adverb modifying the location phrase. Literally, it is something like in the room above.

Yes, that is possible, but the nuance is slightly different.

• en la ĉambro supre = in the room upstairs / in the room above
• en la supra ĉambro = in the upper room / in the upstairs room

The first uses the adverb supre.
The second uses the adjective supra = upper.

Both are natural, but en la ĉambro supre is very common when you are simply identifying the room by its position.

In practice, it most naturally tells you where the books are:

• the wet books in the room upstairs

So the most likely reading is that they came early to save the wet books that were in the upstairs room.

But as in English, context can affect how tightly a phrase attaches. Esperanto word order is flexible, yet here the most natural interpretation is that en la ĉambro supre goes with la malsekajn librojn.

Because both infinitives are coordinated by kaj and share the same purpose phrase.

So:

• por ripari la tegmenton kaj savi la malsekajn librojn
  means
• in order to repair the roof and save the wet books

You could repeat por, but it is not necessary:

• por ripari la tegmenton kaj por savi...

The version with only one por is more economical and very normal.

This sentence is a great example of Esperanto’s regular endings:

• -o = noun → tegmento, ĉambro
• -a = adjective → malseka
• -e = adverb → frue, supre
• -i = infinitive → ripari, savi
• -is = past tense verb → venis
• -j = plural → laboristinoj, libroj
• -n = accusative/direct object → tegmenton, librojn, malsekajn

Once you learn these endings, a sentence like this becomes much easier to unpack.