Mama usiadła przy drzwiach i pomogła córce zawiązać sznurówki.

Usiadła is the past tense, feminine singular form of usiąść, which means to sit down.

So here it tells us that:

• the action happened in the past,
• the subject is feminine,
• and the subject is one person.

Because mama is grammatically feminine, the verb must match it:

• usiadł = he sat down
• usiadła = she sat down

Also, usiąść / usiadła is perfective, so it describes a completed action: she sat down (not just was sitting).

Because przy takes the locative case.

The noun drzwi changes in the locative:

• nominative: drzwi
• locative: drzwiach

So:

• przy drzwiach = by / near / at the door

This is a very useful pattern to remember:

• przy stole = at the table
• przy oknie = by the window
• przy drzwiach = by the door

Because Polish drzwi is a plural-only noun. This is called plurale tantum.

Even when English uses singular door, Polish normally uses plural drzwi:

• te drzwi = this door / these doors, depending on context

That is why the forms look plural:

• nominative: drzwi
• genitive: drzwi
• locative: drzwiach

So przy drzwiach is completely normal Polish for by the door.

Because the verb pomóc / pomagać takes the dative case, not the accusative.

So:

• pomóc komu? czemu? = to help whom? what? in the dative
• córka becomes córce

Forms:

• nominative: córka = daughter
• dative: córce = to the daughter

That is why Polish says:

• pomogła córce = she helped her daughter / the daughter

This is a very common thing learners need to memorize: some verbs simply require a particular case.

Córce is the indirect object.

It tells us who received the help:

• Mama pomogła córce = Mother helped her daughter

So even though English just says helped her daughter, Polish marks that relationship with the dative.

You can think of it roughly as:

• She gave help to her daughter

That is why dative is used.

Because Polish often uses pomóc + infinitive to say help someone do something.

Pattern:

• pomóc komuś + infinitive

So:

• pomogła córce zawiązać sznurówki = she helped her daughter tie her shoelaces

Other examples:

• Pomogłem mu otworzyć drzwi. = I helped him open the door.
• Pomogła mi znaleźć klucze. = She helped me find the keys.

This is a very natural construction in Polish.

Because zawiązać is the perfective infinitive, meaning the action is viewed as completed.

Here the idea is:

• she helped her daughter tie the shoelaces, meaning get them tied

Compare:

• zawiązać = to tie, to get tied, to tie up completely
• zawiązywać = to be tying / to tie repeatedly / to tie in an ongoing sense

After pomóc, the perfective infinitive is very common when the result matters:

• pomóc napisać list = help write the letter
• pomóc ugotować obiad = help cook dinner
• pomóc zawiązać sznurówki = help tie the shoelaces

Sznurówki is the accusative plural of sznurówka.

Singular:

• nominative: sznurówka = shoelace
• accusative: sznurówkę

Plural:

• nominative: sznurówki
• accusative: sznurówki

Because sznurówki is a non-masculine-personal noun, the accusative plural looks the same as the nominative plural.

So in:

• zawiązać sznurówki it means to tie the shoelaces

In real life, people usually tie shoelaces in the plural, because shoes normally have two laces or a pair of laces. So sznurówki is the natural choice.

You could use the singular sznurówkę if you really mean one lace:

• zawiązać sznurówkę = tie one shoelace

But in ordinary situations, Polish often uses the plural:

• zawiązać sznurówki = tie the shoelaces

Because Polish often leaves out possessive words like her, his, my, etc. when the meaning is clear from context.

So:

• pomogła córce zawiązać sznurówki

naturally means:

• she helped her daughter tie her shoelaces

Polish does not need to say jej if there is no ambiguity.

If you add jej, it can sound more explicit or contrastive:

• pomogła jej córce = helped her daughter
• zawiązać jej sznurówki = tie her shoelaces

But in a simple sentence like this, leaving it out is normal.

Przy often means something like:

• by
• near
• at
• next to

The exact English translation depends on context.

So przy drzwiach could be translated as:

• by the door
• near the door
• at the door

All of those are reasonable in English. The Polish preposition gives a general idea of closeness, not necessarily exact physical contact.

The word order is quite natural and neutral:

• Mama usiadła przy drzwiach i pomogła córce zawiązać sznurówki.

Polish word order is more flexible than English because cases show grammatical roles. But this order sounds normal:

1. subject: Mama
2. first action: usiadła przy drzwiach
3. second action: i pomogła córce zawiązać sznurówki

You can change the order for emphasis, for example:

• Przy drzwiach mama usiadła i pomogła córce zawiązać sznurówki.

That puts more focus on by the door. But the original sentence is the most straightforward.

Because both verbs refer to the same subject: Mama.

In Polish past tense, verbs agree with the subject in gender and number:

• mama usiadła
• mama pomogła

If the subject were masculine, you would get:

• Tata usiadł i pomógł.

If it were plural:

• Rodzice usiedli i pomogli.

So the -ła ending is a clear sign of a feminine singular subject in the past tense.

Here Mama is simply the ordinary Polish word for mum / mom.

It is capitalized because it is at the beginning of the sentence, not because it must always be capitalized.

Inside a sentence, you would usually write:

• moja mama
• mama usiadła przy drzwiach

But in direct address, capitalization may also appear depending on style:

• Mamo, chodź tutaj! = Mum, come here!

So in this sentence, the capital M is just normal sentence-initial spelling.