Puella in scalis sedet, quia gradus frigidi pedes eius laedunt.

Latin does not have definite or indefinite articles, so there is no separate word for the or a/an.

So:

• Puella can mean girl or the girl
• gradus frigidi can mean cold steps or the cold steps

You work out which English article to use from the context.

Because Latin prepositions do not always match English prepositions one-for-one.

Here in scalis is an idiomatic way to say that someone is located on the stairs/on the steps. English prefers on, but Latin often uses in for location where English would not.

So the important thing is:

• translate the phrase naturally in English
• do not expect in always to mean only in

Because in takes the ablative when it means in/on/at and shows location, not movement.

Compare:

• in scalis sedet = she sits on the stairs → location → ablative
• if there were movement into or onto something, Latin would often use in with the accusative

So here scalis is ablative plural because the girl is already there, sitting.

Latin often uses the simple present where English prefers a progressive form.

So:

• sedet literally is sits
• but in context it is naturally translated as is sitting

This is very common. Latin does not need a separate word for is plus a participle here.

They are related but not identical in feel.

• scalae / scalis refers to stairs or a stairway
• gradus refers more to the individual steps or treads

So the sentence works like this:

• Puella in scalis sedet = The girl is sitting on the stairs
• quia gradus frigidi... = because the cold steps...

This is also a natural way to avoid repeating exactly the same word twice.

Here it is plural: the steps.

This is a classic point of confusion because gradus is a fourth-declension noun, and without macrons some of its forms look the same in writing.

What tells you it is plural here?

• frigidi is plural
• laedunt is plural

So gradus frigidi must mean the cold steps.

With macrons, the nominative plural would be written gradūs, but many texts leave macrons out.

Because of agreement and the verb ending.

• laedunt = they hurt → plural verb
• frigidi = nominative masculine plural
• gradus matches that adjective

So gradus frigidi is the plural subject: the cold steps.

Meanwhile pedes is the direct object, the thing being hurt.

Latin word order is flexible, so you cannot rely only on position. Endings matter more than word order.

Pedes is accusative plural from pes, pedis (foot).

It is accusative because it is the direct object of laedunt:

• gradus frigidi = the cold steps
• laedunt = hurt
• pedes eius = her feet

So: The cold steps hurt her feet.

Because suus/sua/suum is reflexive and normally refers back to the subject of its own clause.

In the clause:

• gradus frigidi pedes eius laedunt

the subject is gradus frigidi (the cold steps), not puella.

So:

• suos pedes would mean the steps are hurting their own feet, which makes no sense
• eius means her/his/its, referring to someone else, here the girl

So pedes eius correctly means her feet.

Yes. Latin word order is flexible, so both are possible.

• pedes eius
• eius pedes

Both can mean her feet.

In this sentence, pedes eius is perfectly normal. Latin often places the genitive after the noun it modifies.

In Latin, adjectives can come before or after the noun. Word order is much freer than in English.

So both of these are possible in principle:

• gradus frigidi
• frigidi gradus

The endings show the relationship, not just the position:

• gradus = masculine plural nominative here
• frigidi = masculine plural nominative, agreeing with it

So the phrase means cold steps no matter which comes first.

Because this sentence gives a straightforward, real reason:

• quia gradus frigidi pedes eius laedunt
• because the cold steps hurt her feet

With quia, Latin often uses the indicative when the speaker presents the reason as a fact. That is exactly what is happening here.

For a beginner, the simplest rule is:

• quia commonly introduces a reason
• in ordinary statements like this, it usually takes the indicative

Yes:

• Puella — nominative singular, girl; subject of sedet
• in — preposition; here it takes the ablative and means in/on
• scalis — ablative plural of scalae/scala, stairs/steps
• sedet — 3rd person singular present active indicative of sedere, sits / is sitting
• quia — because
• gradus — nominative plural here, from gradus, -us (4th declension), steps
• frigidi — nominative masculine plural of frigidus, agreeing with gradus, cold
• pedes — accusative plural of pes, pedis, feet
• eius — genitive singular, his/her/its; here her
• laedunt — 3rd person plural present active indicative of laedere, hurt / injure

So the structure is:

• Puella ... sedet = The girl is sitting...
• quia gradus frigidi pedes eius laedunt = because the cold steps hurt her feet.