Я взяла одну слойку к чаю.

Because the speaker is female.

In the past tense, Russian verbs change for gender in the singular:

• masculine: взял
• feminine: взяла
• neuter: взяло
• plural: взяли

So Я взяла means I took said by a woman.
A man would say Я взял одну слойку к чаю.

The basic dictionary form is взять, which means to take.

взяла is the feminine singular past-tense form of взять.

This verb is perfective, so it usually refers to a completed action: the speaker took one pastry as a finished act.

Its imperfective partner is брать:

• Я брала... = I was taking / I used to take
• Я взяла... = I took

Because слойку is the direct object of the verb взяла, so it is in the accusative case.

The noun слойка is feminine, and feminine nouns ending in -а often change like this:

• nominative: слойка
• accusative: слойку

The number one must agree with the noun, so it also changes:

• nominative: одна
• accusative feminine: одну

So:

• одна слойка = one pastry (subject form / dictionary-style form)
• взяла одну слойку = took one pastry

Because one in Russian behaves a lot like an adjective: it changes for gender, number, and case.

Forms of one in the nominative:

• masculine: один
• feminine: одна
• neuter: одно

But here we need the accusative feminine singular, because it modifies слойку, which is feminine and is a direct object. So одна becomes одну.

Слойка usually means a flaky pastry, often made from puff pastry.

Depending on context, it can refer to:

• a plain puff pastry
• a sweet pastry
• a filled pastry, such as with jam, apple, or cheese

So it is a fairly ordinary food word, not some unusual grammar example.

Literally, к чаю means to tea, but in natural English it usually means something like:

• for tea
• to go with tea
• with tea

This is a common Russian expression. It often refers to food you have along with tea, especially a snack, pastry, sweets, or cake.

Examples:

• Что купить к чаю? = What should we buy for tea?
• У нас есть печенье к чаю. = We have cookies to go with tea.

So одну слойку к чаю means the pastry was taken as something to have with tea.

Because the preposition к requires the dative case.

The noun чай changes like this:

• nominative: чай
• dative: чаю

So:

• к чаю = for tea / to go with tea

This is a very common pattern:

• к кофе = for coffee
• к супу = with soup / for the soup
• к ужину = for dinner

Not always in a narrow literal sense.

Very often it does involve actual tea, but culturally it can also imply something nice to snack on, especially in a home setting. In many contexts, it is close to saying:

• something for tea
• something sweet to have with tea
• a tea-time snack

So the phrase can carry a small cultural nuance, not just a strictly word-for-word meaning.

Yes. Russian word order is flexible, though the most neutral version here is:

Я взяла одну слойку к чаю.

Other orders are possible, for example:

• Одну слойку к чаю я взяла.
• К чаю я взяла одну слойку.

These can shift emphasis:

• starting with К чаю emphasizes for tea
• starting with Одну слойку emphasizes one pastry

But for a plain, neutral statement, the original word order is very natural.

Not always. Russian often drops subject pronouns when the meaning is clear from the verb form or context.

So you could also say:

• Взяла одну слойку к чаю.

Because взяла already shows feminine singular past, the listener may understand I from context.

Still, я is perfectly normal and may be included for clarity, contrast, or emphasis.

Yes. Взять specifically means to take. It does not by itself mean to buy or to eat.

So:

• взяла = took
• купила = bought
• съела = ate

In context, взяла could mean physically took it from a plate, shelf, tray, or display. The sentence only tells us that the speaker took one pastry for tea; it does not say whether she bought it, ate it, or merely picked it up.