Piscator rete novum ad navem portat.

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

Also, the verb portat means he/she/it carries or is carrying, so it matches a third-person singular subject. Piscator is one person, so it fits.

Rete is the thing being carried, so it is the direct object.

A learner might expect the object to have a special ending, but here rete is a neuter third-declension noun. In many neuter nouns, the nominative and accusative singular look the same. So rete can be either nominative or accusative depending on its job in the sentence. Here, its job is object, so it is accusative singular.

Because novum agrees with rete.

Latin adjectives must agree with the noun they describe in:

• gender
• number
• case

Rete is:

• neuter
• singular
• accusative

So the adjective must also be:

• neuter
• singular
• accusative

That gives novum.

Ad navem is a prepositional phrase showing direction: movement toward or to the ship.

So it answers a question like Where is he carrying it? or To where?

It is not the direct object. The direct object is rete.
Ad navem just adds the destination.

Because the preposition ad takes the accusative case.

The dictionary form is navis, but after ad it becomes navem, which is the accusative singular.

So:

• navis = nominative singular
• navem = accusative singular

This is very common in Latin: a preposition determines the case of the noun that follows it.

Portat is:

• present tense
• active voice
• indicative mood
• third person singular

It comes from porto, portare, meaning to carry.

So portat means:

• he carries
• she carries
• it carries
• or in smoother English, is carrying

Latin does not need a separate word for he or she here, because the verb ending -t already shows third person singular.

Because Latin has no articles.

So a Latin noun like piscator can mean:

• a fisherman
• the fisherman

and rete can mean:

• a net
• the net

The exact choice in English depends on context.

Less than in English.

Latin relies heavily on word endings, so the sentence can often be rearranged without changing the basic meaning. For example, these would still mean essentially the same thing:

• Piscator rete novum ad navem portat
• Rete novum piscator ad navem portat
• Ad navem piscator rete novum portat

The version you were given is a very natural Latin order, with the verb at the end, which is especially common.

Yes. Latin adjectives can often come before or after the noun.

So both of these are possible:

• rete novum
• novum rete

Sometimes word order gives a slightly different emphasis, but both are grammatically fine.

Because ad navem is clearly a prepositional phrase, not an adjective.

It tells you the destination of the action, not a quality of the net. In other words, it belongs with the action portat, not with the noun the way novum does.

So:

• novum describes what kind of net
• ad navem shows where it is being carried

Here are the usual dictionary forms:

• piscator, piscatoris — fisherman
• rete, retis — net
• novus, nova, novum — new
• ad — to, toward
• navis, navis — ship
• porto, portare, portavi, portatum — carry

A learner should get used to the fact that the form in the sentence is often not the same as the dictionary form.

Not exactly.

In English, an indirect object is something like to the sailor in he gives the net to the sailor.

But ad navem is not an indirect object. It is a prepositional phrase of motion toward a place. The ship is the destination, not a recipient in the grammatical sense.

So it is better to think of ad navem as to the ship / toward the ship, not as an indirect object.