К тому же у них сегодня скидка, и кассир дала мне ещё одну закладку.

К тому же means besides that, on top of that, or what’s more.

It is used to add another piece of information that supports what was just said. In this sentence, it introduces an extra benefit:

• К тому же у них сегодня скидка = Besides that, they have a discount today

It is a fixed expression, so it is best learned as a chunk.

Russian very often expresses having with у + genitive rather than with a verb meaning to have.

So:

• у них скидка literally means at them there is a discount
• natural English: they have a discount

This pattern is extremely common:

• У меня есть книга = I have a book
• У нас проблема = We have a problem
• У них сегодня скидка = They have a discount today

Here, них is the genitive form of они after the preposition у.

Because у is a preposition, and it requires the genitive case.

The pronoun они changes like this:

• nominative: они = they
• genitive after у: них

So:

• они = they
• у них = at them / they have

This is not optional; after у, you need the correct case form.

In the pattern у кого-то есть что-то or у кого-то что-то, the thing that exists is normally in the nominative case.

So in:

• у них сегодня скидка

the noun скидка is the thing that exists, so it stays nominative singular.

Compare:

• У меня машина = I have a car
• У нас урок = We have a lesson
• У них скидка = They have a discount

Скидка means discount or sale reduction.

So:

• сегодня скидка = there is a discount today / today they’re offering a discount

Depending on context, it could mean a general sale, a reduced price, or a special offer.

Because the verb agrees with the actual gender of the person, not with the grammatical form of the job title alone.

Кассир is a noun meaning cashier. It often has the same form for a man or a woman in everyday usage. The past tense verb shows the gender:

• кассир дал = the cashier gave, if the cashier was male
• кассир дала = the cashier gave, if the cashier was female

So дала tells you that the cashier was a woman.

Мне is the dative case of я, and it is used for the recipient of the action.

In:

• кассир дала мне ещё одну закладку

the cashier gave to me another bookmark, so Russian uses the dative:

• я = I
• мне = to me

This is very common with verbs of giving:

• дать кому? = to give to whom?
• сказать кому? = to say to whom?
• показать кому? = to show to whom?

Because закладку is the direct object, so it is in the accusative case, and the numeral/adjective-like word одну must agree with it.

Base form:

• одна закладка = one bookmark

After the verb дала:

• дала одну закладку = gave one bookmark

Since закладка is a feminine singular animate? No, it is inanimate, but feminine nouns in the accusative singular often change form anyway:

• nominative: закладка
• accusative: закладку

And одна also changes to match:

• nominative feminine: одна
• accusative feminine: одну

So:

• ещё одну закладку = another / one more bookmark

Here it means another one or one more.

So:

• кассир дала мне ещё одну закладку = the cashier gave me one more bookmark

Ещё can have several meanings depending on context:

• still: Он ещё дома = He is still at home
• more / another: ещё чай = more tea
• one more / another one: ещё одну закладку

In this sentence, the another / one more meaning is the natural one.

Most likely it means bookmark.

So the sentence probably means the cashier gave the speaker an extra bookmark, perhaps as a free item from a bookstore.

Be aware that закладка can have other meanings in different contexts, but bookmark is the most likely one here.

In the present tense, Russian often leaves out есть when the meaning is clear.

So both of these are possible:

• У них сегодня есть скидка
• У них сегодня скидка

The version without есть is very natural and common, especially in simple statements.

So literally Russian may look shorter than English, but the meaning is still:

• They have a discount today

Yes. Russian word order is flexible, and сегодня can often move depending on emphasis.

For example:

• У них сегодня скидка
• Сегодня у них скидка

Both are natural. The difference is mainly in focus:

• У них сегодня скидка emphasizes with them / at their place
• Сегодня у них скидка emphasizes today

In your sentence, the chosen order sounds very natural.

Not exactly. A more literal breakdown is:

• К тому же = besides that
• у них сегодня скидка = at them today discount
• и кассир дала мне ещё одну закладку = and the cashier gave to me one more bookmark

Natural English smooths this out as:

• Besides that, they have a discount today, and the cashier gave me another bookmark.

So the meaning matches English, but some of the grammar patterns are different, especially у них for they have and мне for to me.