Senator prudens dicit cives bonum commune commodo privato praeferre debere.

Because prudens describes senator, and adjectives must agree with the nouns they modify in case, number, and gender.

• senator = nominative singular masculine
• prudens = nominative singular masculine (or feminine in form, but here masculine in meaning because it describes senator)

So senator prudens means the wise/prudent senator.

Prudens is an adjective meaning wise, prudent, or sensible.

It belongs to the third declension, so it does not look like a first-and-second-declension adjective such as bonus, bona, bonum. Its nominative singular masculine and feminine are both prudens.

That is why Latin says:

• senator prudens = a wise senator

not something like senator prudus.

Because Latin often expresses reported speech or thought with an accusative-and-infinitive construction instead of a subordinate clause with that.

So:

• dicit = he says
• cives ... debere = that the citizens ought ...

Literally, Latin is doing something more like:

• The senator says the citizens to ought to prefer...

That sounds wrong in English, so we translate it naturally as:

• The wise senator says that the citizens ought to prefer...

In Latin indirect statement, the subject of the infinitive goes into the accusative.

So in this sentence:

• cives is accusative plural
• it is the logical subject of debere
• and also the people who are doing the action of praeferre

So cives ... praeferre debere means:

• that the citizens ought to prefer...

This is one of the most important Latin constructions for English speakers to learn.

Because they work together.

• debere = to ought / to be obliged
• praeferre = to prefer

So praeferre debere means to ought to prefer or, in normal English, ought to prefer / should prefer.

Inside the indirect statement, Latin uses the infinitive debere, and debere itself takes the complementary infinitive praeferre.

So the structure is:

• dicit = he says
• cives ... debere = that the citizens ought
• praeferre = to prefer

Because it is the direct object of praeferre.

The verb praeferre means to place before, and from that comes the sense to prefer. In this construction, the thing being preferred is put in the accusative.

So:

• bonum commune = the common good
• case: accusative singular neuter

It is what the citizens ought to prefer.

Because praeferre commonly takes a dative for the thing to which something else is preferred.

So the pattern is:

• aliquid alicui praeferre = to prefer something to something

In this sentence:

• bonum commune = the thing preferred
• commodo privato = the thing it is preferred to

So:

• bonum commune commodo privato praeferre
  = to prefer the common good to private advantage

The endings show it.

• commodo = dative singular of commodum
• privato = dative singular of privatus agreeing with commodo

Since both words are dative singular neuter, they go together as a phrase:

• commodo privato = to private advantage / to private benefit

And because praeferre uses the dative for the thing compared against, that tells you how the phrase functions.

It is a noun phrase made from:

• bonum = good (used substantively, or as a noun-like adjective)
• commune = common, agreeing with bonum

Together they mean:

• the common good

Both are accusative singular neuter, since they are the object of praeferre.

This is a very common Latin expression in political and moral writing.

Because classical Latin has no articles.

So:

• senator can mean a senator or the senator
• cives can mean citizens or the citizens
• bonum commune can mean the common good

English has to choose whether to use a/an or the, but Latin usually leaves that to context.

The word order is meaningful, but Latin is much freer than English because the endings show the grammatical relationships.

This sentence could be rearranged in several ways without changing the basic meaning, for example:

• Prudens senator dicit cives bonum commune commodo privato praeferre debere.
• Cives senator prudens dicit bonum commune commodo privato praeferre debere.

The original order is fairly natural and readable:

• Senator prudens introduces the speaker
• dicit gives the main verb
• then the indirect statement follows

So English speakers should pay more attention to endings and constructions than to position alone.

A natural translation is:

• The wise senator says that citizens ought to prefer the common good to private advantage.

You could also translate debere a bit differently depending on context:

• The wise senator says that citizens should prefer the common good to private interest.
• The prudent senator says that citizens must put the common good before private benefit.

All of these reflect the same Latin structure.

Yes, very closely. In fact, English prefer ultimately comes from the same Latin verb praeferre.

Latin:

• prae- = before
• ferre = to carry / bear

So literally praeferre is to carry before or to place before, and from that it comes to mean to prefer.

That is why the construction feels slightly different in Latin:

• to place X before Y
• therefore to prefer X to Y

So in this sentence the citizens are being said to put the common good before private advantage.