Discipula chartam in mensa ponit et stilum quaerit.

Because discipula is in the nominative singular, which is the case normally used for the subject of a sentence.

Also, both verbs — ponit and quaerit — are 3rd person singular, so they match one singular subject. That tells you that discipula is the one doing both actions.

Because chartam is the direct object of ponit.

In Latin, a direct object usually goes in the accusative case.
So:

• charta = nominative singular
• chartam = accusative singular

Since the student is putting the paper, Latin uses chartam.

For the same reason: stilum is the direct object of quaerit.

The thing being searched for is put in the accusative case, so:

• stilus = nominative singular
• stilum = accusative singular

English mostly shows this by word order, but Latin shows it with the ending.

This is a very common question.

The basic rule is:

• in
  • ablative = in/on a place
• in
  • accusative = motion into/onto a place

So in mensā literally means on the table or in the table-place, while in mēnsam would more strongly mean onto the table.

Because ponit is a verb of placing, many learners expect in mensam here. In very strict classical usage, that would often be the more expected way to show motion onto the table. But beginner materials sometimes use in mensa to focus on the location where the object ends up: on the table.

So your instinct is reasonable: this is exactly the kind of phrase learners often stop and ask about.

Because Latin has no articles.

Latin does not have separate words for the or a/an. Whether a noun is definite or indefinite is usually understood from context.

So:

• discipula can mean the student or a student
• chartam can mean the paper or a paper
• stilum can mean the stylus/pen or a stylus/pen

English must choose; Latin usually does not.

They are both present active indicative, 3rd person singular.

That means:

• ponit = she puts / is putting / does put
• quaerit = she looks for / is looking for / does look for

In simple beginner sentences, the usual English translation is just puts and looks for.

Because the same subject is understood to continue.

Latin often leaves out a repeated subject when it is obvious. Since et joins two verbs, the sentence naturally means that the student both puts the paper down and looks for the stylus.

So Latin does not need to say discipula ... et discipula ...

Et means and. It connects the two actions:

• chartam in mensa ponit
• stilum quaerit

So one subject, discipula, is doing two things in sequence or as part of the same scene.

Not as much as in English.

English relies heavily on word order: The student puts the paper...
Latin relies much more on endings:

• discipula = subject form
• chartam and stilum = object forms

Because of that, Latin word order is more flexible. This sentence uses a very normal order, but other arrangements are possible for emphasis.

For example, Latin could move words around and still keep the same basic meaning, because the endings still show each word’s job.

Yes. Discipula is a feminine noun, so it means a female student / schoolgirl / female pupil.

The masculine form would be discipulus.

This matters for vocabulary and sometimes for agreement with adjectives, but in this sentence the verbs themselves do not change form for gender. Ponit and quaerit can mean he, she, or it depending on the subject.

They belong to standard Latin declensions:

• discipula — 1st declension
• charta — 1st declension
• mensa — 1st declension
• stilus — 2nd declension

That helps explain their endings:

• -a / -am for many 1st-declension singular forms
• -us / -um for many 2nd-declension masculine singular forms

So the sentence is also giving you practice in recognizing common noun patterns.

They come from:

• ponit ← ponere = to put, place
• quaerit ← quaerere = to seek, look for, ask for

Both are commonly taught as 3rd-conjugation verbs. In this sentence, each appears in the present tense, 3rd person singular.

So if you are learning dictionary forms, the verb entries to remember are ponere and quaerere.