На берегу дочка нашла большую ракушку и начала строить песочный замок с маленьким ведёрком.

Because берег has a special location form after на and в: на берегу = on the shore.

This is often called the locative or second prepositional. A small group of masculine nouns uses -у / -ю in fixed expressions of location:

• на берегу = on the shore
• в лесу = in the forest
• в саду = in the garden

But in other prepositional uses you may get the regular form:

• о береге = about the shore

So here на берегу is the normal idiomatic form.

Дочка is a more affectionate, everyday word than дочь.

• дочь = daughter, neutral or more formal
• дочка = daughter / little daughter, warmer and more conversational

Russian often uses diminutive-like forms for family members and children, even when English would just say daughter.

So дочка does not always have to mean a very small child; it often just sounds more natural and affectionate.

Because the subject, дочка, is feminine singular, and Russian past tense agrees with the subject in gender and number.

Compare:

• нашёл, начал = masculine singular
• нашла, начала = feminine singular
• нашло, начало = neuter singular
• нашли, начали = plural

So the -а ending tells you that a female person did the action.

Because this is the direct object of нашла (found), so it must be in the accusative case.

Base form:

• большая ракушка = a big seashell

After нашла:

• нашла большую ракушку = found a big seashell

The changes are:

• большая → большую
• ракушка → ракушку

This is the normal accusative singular pattern for feminine nouns in -а / -я and their adjectives.

It actually is in the accusative, but for a masculine inanimate singular noun, the accusative often looks exactly like the nominative.

So:

• nominative: песочный замок
• accusative: строить песочный замок

They look the same.

That is normal for masculine inanimate nouns. Compare with an animate noun, where you would see a different form:

• я вижу брата = I see my brother

But with замок (castle), which is inanimate, accusative = nominative.

Because after начать (to begin / to start), Russian normally uses the infinitive.

So:

• начала строить = started to build

Not:

• начала строила ❌

This is the same basic idea as in English:

• She began building
• She started to build

In Russian, начала + infinitive is the standard pattern.

This is about aspect, which is very important in Russian.

• нашла is from найти (perfective)
  It presents the finding as a completed event: she found it.

• начала is from начать (perfective)
  It presents the start as a completed event: she started.

• строить is imperfective
  It focuses on the process/activity of building, not on finishing the castle.

So the sentence means roughly:

• she found the shell
• and started building a sandcastle

It does not say she finished building it.

That is why строить is the natural choice here.

Normally, no. Начать usually combines with an imperfective infinitive when you mean start doing something.

So:

• начала строить = correct, natural

But:

• начала построить = generally unnatural in this meaning

Why? Because построить is perfective and means build/finish building as a complete result. After начать, Russian usually wants the verb of the ongoing action, not the completed whole event.

Because the preposition с here means with, and it requires the instrumental case.

Base form:

• маленькое ведёрко = a little bucket

After с:

• с маленьким ведёрком = with a little bucket

The forms change like this:

• маленькое → маленьким
• ведёрко → ведёрком

In context, this most naturally means she was building the sandcastle using the little bucket.

Grammatically, с + instrumental can sometimes suggest either accompaniment or means/tool, depending on context.

Here, the natural interpretation is using the bucket:

• she started building a sandcastle with a little bucket

Because of the situation, Russian speakers will normally understand it as the bucket being the tool.

Ведёрко is a diminutive form of ведро (bucket).

So:

• ведро = bucket
• ведёрко = little bucket / cute little bucket

The letter ё is pronounced like yo and is always stressed.

So:

• ведёрко
• ведёрком

In many Russian texts, ё is often written as е, so you might also see:

• ведерко
• ведерком

But the pronunciation is still ведёрко, ведёрком.

For sandcastle, the normal expression is песочный замок.

Both песочный and песчаный relate to sand, but they are used differently:

• песочный often means made of sand or connected with sand in a practical/everyday way
• песчаный often describes something sandy in a more material or natural sense, like песчаный берег (sandy shore)

So песочный замок is the standard phrase for sandcastle.

Russian word order is fairly flexible, and putting На берегу first sets the scene:

• На берегу = on the shore

So the sentence begins with the location, then moves to what happened there.

A more neutral English-like order would also be possible:

• Дочка нашла на берегу большую ракушку...

But starting with На берегу gives a natural storytelling feel, like:

• On the shore, the daughter found...

So the first position is mostly about focus and style, not a different basic meaning.

Russian has no articles, so it does not have separate words for a and the.

That means forms like:

• дочка
• ракушку
• замок

can mean a daughter / the daughter, a shell / the shell, a castle / the castle, depending on context.

Russian speakers understand definiteness from:

• context
• word order
• shared knowledge
• the situation being described

So in this sentence, the exact English choice (a or the) comes from context, not from a separate Russian word.