Discipula bibliothecam desiderat, quia diu domi manere debet.

Because discipula is in the nominative singular, the case normally used for the subject.

• discipula = the female student / schoolgirl
• It ends in -a, which for a first-declension noun is often the nominative singular ending.

So in Discipula bibliothecam desiderat, discipula is the one doing the action.

Because bibliothecam is the direct object of desiderat, so it is in the accusative singular.

• bibliotheca = library in the dictionary form
• bibliothecam = library as the object of the verb

Latin marks jobs in the sentence with endings. English usually relies more on word order, but Latin often shows the object by the accusative ending instead.

Desiderat is the third person singular present active indicative of desiderare.

It means:

• she desires
• she longs for
• sometimes she misses

In this sentence, it means that the student longs for / misses the library. The exact English wording depends on the translation you were given, but the grammar is the same.

Because Latin does not have articles like English the and a/an.

So:

• discipula can mean a student or the student
• bibliothecam can mean a library or the library

You decide which English article fits best from the context.

Quia means because and introduces a clause giving the reason.

So the sentence breaks into two parts:

• Discipula bibliothecam desiderat = the main statement
• quia diu domi manere debet = the reason, because she must stay at home for a long time

This is very similar to English because.

This is a very common Latin construction:

• debet = she ought / she must / she is supposed to
• manere = to stay / to remain

Together, manere debet means she must stay or she ought to remain.

Latin often uses debeo + infinitive the way English uses must, ought to, or sometimes have to.

The subject is still discipula.

Latin often leaves out subject pronouns when they are clear from the verb ending or context. Here:

• debet = she must
• so the understood subject of manere is the same person, the student

In other words, quia diu domi manere debet means because she must stay at home for a long time.

Domi is a special form meaning at home.

With domus and with the names of cities, small islands, and a few special words, Latin can use the locative, which expresses place where.

So:

• domi = at home
• domum = homeward / to home
• domo = from home

In this sentence, the meaning is at home, so domi is correct.

Diu is an adverb meaning for a long time or for a long while.

It modifies manere debet, telling you how long she must stay at home.

Latin adverbs are often fairly flexible in position. Here diu comes before domi manere debet, but the basic meaning would stay the same if the word order changed.

Latin word order is more flexible than English word order because the endings show what each word is doing.

In English, we depend heavily on order:

• The student misses the library

If we switch the words around, the meaning changes or becomes unclear.

In Latin, endings help us identify the subject and object:

• discipula = subject
• bibliothecam = object

So Discipula bibliothecam desiderat is clear even if the order changes. Latin often places the verb near the end, especially in straightforward prose, but other orders are possible for emphasis.

Both finite verbs are present indicative active:

• desiderat = she desires / misses
• debet = she must / ought

And manere is a present active infinitive.

So the structure is:

• present indicative main verb: desiderat
• present indicative verb in the quia clause: debet
• infinitive depending on debet: manere

This is all normal, direct statement Latin, not subjunctive or anything more complicated.