Antequam nuptiae incipiant, magistra, quae etiam propinqua est, puellis dicit bonos mores in omni domo servandos esse.

Because nuptiae is normally a plural noun in Latin. It refers to a wedding / marriage ceremony, even though the English equivalent is often singular.

So:

• nuptiae = wedding, nuptials
• incipiant is plural because it agrees with nuptiae

Latin is literally saying something like before the nuptials begin, but natural English is usually before the wedding begins.

After antequam (before), Latin can use either the indicative or the subjunctive, depending on the sense.

Here the subjunctive fits because the action is still anticipated or not yet realized from the point of view of the main clause:

• Antequam nuptiae incipiant = before the wedding begins

The idea is not just a plain fact, but something still in the future relative to dicit. So incipiant is a very natural choice.

Quae refers to magistra.

It is:

• feminine singular
• nominative
• the subject of est

It has to match the noun it refers to:

• magistra = feminine singular
• therefore quae = feminine singular

So magistra, quae etiam propinqua est means the teacher, who is also a relative.

Because quae is doing two jobs at once:

1. It agrees with its antecedent, magistra, in gender and number
2. Its case depends on its role inside the relative clause

Inside the clause quae etiam propinqua est, the pronoun is the subject of est, so it must be nominative.

That is why Latin uses quae:

• feminine singular nominative = quae

Latin often lets an adjective function almost like a noun when the meaning is clear.

So propinqua here means:

• a female relative
• or more literally related

In this sentence it is a predicate word after est:

• quae etiam propinqua est = who is also a relative

Because it refers back to magistra, it is feminine singular.

Because dico commonly takes the person being told in the dative.

So:

• magistra puellis dicit = the teacher says to the girls / tells the girls

Here:

• magistra = subject
• puellis = indirect object, to the girls

This is very normal Latin usage with verbs of speaking.

Because it is the subject of an indirect statement after dicit.

Latin often uses:

• verb of saying/thinking/perceiving
• plus accusative + infinitive

So in:

• dicit bonos mores ... servandos esse

the phrase bonos mores is the logical subject of servandos esse, but in Latin indirect statement that subject goes into the accusative.

So:

• direct idea: boni mores servandi sunt
• indirect after dicit: bonos mores servandos esse

This is a gerundive of obligation with esse, sometimes called the passive periphrastic.

• servandos = gerundive of servo
• esse = infinitive to be

Together they mean something like:

• to have to be preserved
• must be kept
• must be observed

Because it is inside indirect statement after dicit, Latin uses the infinitive esse rather than a finite verb.

And servandos agrees with bonos mores:

• masculine
• plural
• accusative

A normal infinitive might simply state an action, such as servare = to preserve.

But servandos esse adds the idea of necessity or obligation.

So:

• bonos mores servare = to preserve good morals
• bonos mores servandos esse = that good morals must be preserved

That extra sense of must / ought to comes from the gerundive.

Because in with the meaning in, inside takes the ablative.

So:

• in omni domo = in every home

Also, domus is a somewhat irregular noun, but domo is the normal ablative singular form here.

So the grammar is:

• in
  • ablative for location
• omni agrees with domo

Mores can cover several related ideas:

• customs
• character
• conduct
• morals
• manners/behavior

In this sentence, with bonos and servandos esse, it most naturally means something like:

• good morals
• good behavior
• proper conduct

So it is broader than just table manners; it refers to the standards of behavior expected in a household.

Latin word order is much more flexible than English word order because the endings show the grammatical relationships.

So Latin can place words for emphasis or style:

• Antequam nuptiae incipiant sets the time first
• magistra is then identified
• quae etiam propinqua est adds extra information about her
• puellis dicit gives the main action
• bonos mores in omni domo servandos esse saves the reported statement for the end

In English, we rely heavily on word order. In Latin, we rely much more on case endings and verb forms.