In villa medica faciem puellae spectat et dicit frontem calidiorem esse quam heri.

A helpful way to read it is:

• In villa = in the house / in the villa
• medica spectat = the female doctor looks at
  (or, depending on context, the subject may be implied and *medica may belong with villa; see below)*
• faciem puellae = the girl's face
• et dicit = and says
• frontem calidiorem esse quam heri = that the forehead is warmer than yesterday

So the sentence has:

• a location phrase,
• a main verb phrase,
• and then a reported statement after dicit.

Because in takes the ablative when it means in or on in the sense of location.

So:

• in villa = in the house
• but in villam would mean into the house

This is a very common Latin pattern:

• in urbe = in the city
• in urbem = into the city

Very likely, yes: medica can mean female doctor, and in that reading it is the subject of spectat and dicit.

So the sentence would mean something like:

• In villa, medica faciem puellae spectat...
• In the house, the female doctor looks at the girl's face...

However, a beginner may notice something important: without macrons, medica can also look like medicā, an ablative adjective meaning medical, so in villa medicā could mean in the medical house/clinic.

So context decides. If the translation you were shown has the doctor as the person doing the looking and speaking, then medica is the subject.

Because Latin uses the genitive case to show possession.

• puella = girl
• puellae = of the girl / the girl's

So:

• faciem puellae = the face of the girl = the girl's face

This is one of the most basic uses of the genitive.

A native English speaker often expects something like an apostrophe, but Latin does not use punctuation that way. It uses case endings instead.

Because they belong to different declensions.

• faciem comes from facies, faciei and is a 5th-declension noun.
• frontem comes from frons, frontis and is a 3rd-declension noun.

Both are singular forms, but Latin nouns do not all make their cases the same way. Different noun families have different patterns.

So the difference in ending does not mean a difference in meaning like English would expect; it mostly reflects the noun’s declension.

Because Latin often leaves the subject pronoun out when the verb ending already tells you the person and number.

• spectat = he/she/it looks at
• dicit = he/she/it says

The ending -t shows 3rd person singular.

Latin usually does not need to add ea or is unless it wants extra emphasis or contrast. English usually needs a subject pronoun; Latin often does not.

Because after verbs of saying, thinking, knowing, hearing, and so on, Latin very often uses an indirect statement construction.

That construction is:

• accusative + infinitive

So instead of saying:

• dicit frontis calidior est (not correct for this structure)

Latin says:

• dicit frontem calidiorem esse

Literally, that is something like:

• she says the forehead to be warmer

But in natural English we translate it:

• she says that the forehead is warmer

So esse is used because Latin is reporting what is said, not giving the statement directly.

Because in an indirect statement, the subject of the infinitive goes into the accusative.

That is one of the most important things to learn about this construction.

So here:

• frontem = the subject of esse
• calidiorem = describes frontem
• esse = infinitive to be

In direct speech, you would expect something like:

• frons calidior est = the forehead is warmer

But after dicit, Latin changes that into indirect statement:

• frontem calidiorem esse

So frontem is accusative not because it is the direct object of warmer, but because it is the accusative subject of the infinitive.

Calidiorem is the comparative form of calidus (warm / hot).

Its basic comparative form is:

• calidior = warmer

Here it is accusative singular, because it agrees with frontem.

So:

• frontem calidiorem = the forehead [to be] warmer

The agreement is in:

• gender: feminine, because frons/frontem is feminine
• number: singular
• case: accusative, because frontem is accusative in the indirect statement

It means than yesterday.

• quam = than
• heri = yesterday

So:

• calidiorem quam heri = warmer than yesterday

This is a comparison. The full idea is:

• warmer than it was yesterday

But Latin often leaves the repeated verb understood.

Because Latin often omits words that are easy to understand from the context.

So quam heri is a shortened way of saying something like:

• quam heri erat
• than it was yesterday

The omitted part is understood automatically.

English can do this too:

• She is happier than yesterday

That is not the fullest possible English sentence, but the meaning is clear. Latin does the same kind of thing.

Because Latin relies much more on endings than on word order to show how words fit together.

English depends heavily on order:

• The doctor sees the girl
• The girl sees the doctor

Latin can move words around more freely because the case endings tell you what each word is doing.

So in this sentence, Latin can place:

• the location first,
• then the subject,
• then the object,
• then the second verb,
• then the whole indirect statement.

That does not confuse a Latin reader the way it would confuse an English reader, because the endings keep the grammar clear.

Because classical Latin has no articles.

So Latin does not normally distinguish with separate words between:

• a girl
• the girl

Instead, the context tells you which is meant.

That is why:

• puella can mean a girl or the girl
• faciem puellae can mean a girl's face or the girl's face

In translation, English has to choose an article, but Latin usually does not need one.