Latrina aquam ad cloacam mittit.

Because latrina is in the nominative singular, which is the case usually used for the subject.

In this sentence:

• latrina = subject
• aquam = direct object
• ad cloacam = a prepositional phrase showing direction
• mittit = verb

So latrina is the thing doing the action of mittit.

Because aquam is the direct object of the verb mittit.

The verb mittit means sends or dispatches, so the question is: sends what?
Answer: aquam = water

In Latin, a direct object usually goes in the accusative case. For a first-declension noun like aqua, the accusative singular ends in -am:

• nominative: aqua
• accusative: aquam

So aquam shows that water is receiving the action.

Because ad is the preposition meaning to or toward, and it shows direction.

So:

• ad = to / toward
• cloacam = sewer in the accusative case

Together, ad cloacam means to the sewer.

Latin often uses a preposition like ad when English uses to.

Because the preposition ad takes the accusative case.

That is a rule you simply learn with the preposition:

• ad + accusative = to / toward

Since cloaca is a first-declension noun, its accusative singular is cloacam.

So the ending is not there because cloaca is the direct object of the sentence. It is accusative because it is the object of the preposition ad.

Mittit is:

• 3rd person
• singular
• present tense
• active voice
• indicative mood

It comes from the verb mittere, meaning to send.

So mittit means he/she/it sends.

Since the subject is latrina, we understand it here as it sends.

Classical Latin does not have definite or indefinite articles like English the, a, or an.

So:

• latrina can mean the toilet or a toilet
• aquam can mean water or the water, depending on context
• cloacam can mean the sewer or a sewer

English usually has to choose an article, but Latin often leaves that unstated.

Yes and no.

This sentence uses a very normal Latin order:

• subject: latrina
• object: aquam
• prepositional phrase: ad cloacam
• verb: mittit

But Latin word order is more flexible than English because the endings show the grammatical roles.

So these could still mean basically the same thing:

• Latrina aquam ad cloacam mittit.
• Aquam latrina ad cloacam mittit.
• Ad cloacam latrina aquam mittit.

The meaning stays clear because of the case endings, though the emphasis may change.

They are all first-declension nouns.

You can tell because their dictionary forms end in -a:

• latrina, latrinae
• aqua, aquae
• cloaca, cloacae

Their singular forms here are:

• nominative singular: latrina
• accusative singular: aquam
• accusative singular: cloacam

This is a useful beginner sentence because all three nouns follow a familiar pattern.

Because the ending of the verb already tells you the person and number.

The ending -it in mittit tells you the verb is 3rd person singular.
That can mean:

• he sends
• she sends
• it sends

The subject noun latrina tells you which one makes sense here, so in English we say it sends.

Latin often does not need a separate subject pronoun.

Yes. The basic meaning of mittere is to send, but in different contexts it can also mean things like:

• let go
• dispatch
• send forth
• throw
• direct

In this sentence, sends is a natural English translation, but the idea is really that the latrine directs or carries water toward the sewer.

In a simple Classical Latin pronunciation, you could say it roughly like this:

• Latrina = lah-TREE-nah
• aquam = AH-kwam
• ad = ahd
• cloacam = kloh-AH-kam
• mittit = MIT-tit

A few helpful points:

• c is always hard, like k
• qu sounds like kw
• ti in mittit is just ti, not English sh

So a rough full pronunciation would be:

lah-TREE-nah AH-kwam ahd kloh-AH-kam MIT-tit

Yes, and that is a very good way to read Latin.

You can divide it like this:

• Latrina = the subject
• aquam = the thing being sent
• ad cloacam = where it is being sent
• mittit = the action

So the structure is:

[subject] [object] [direction] [verb]

Breaking Latin into chunks like this makes sentences much easier to read.