Yeni broşürde üyelik bilgileri açıkça yazıyor.

A word-by-word breakdown is:

• yeni = new
• broşürde = in the brochure / on the brochure
• üyelik = membership
• bilgileri = information/details
• açıkça = clearly
• yazıyor = is written / says / is saying

A natural full translation is:

• The membership information is clearly stated in the new brochure.
• or The new brochure clearly gives the membership details.

Turkish often uses yazıyor in places where English would say it says or it is written.

-de / -da / -te / -ta is the locative ending, meaning in, on, at.

So:

• broşür = brochure
• broşürde = in the brochure / on the brochure

In this sentence, it tells you where the information appears.

Why -de specifically?

• Turkish uses vowel harmony, so after ü, the ending becomes -de
• Turkish also chooses d or t depending on the last consonant of the word
• broşür ends in r, which is voiced, so you use d, not t

So:

• broşür + de -> broşürde

No. In Turkish, adjectives normally do not agree with the noun in case or number.

So:

• yeni broşür = new brochure
• yeni broşürde = in the new brochure

Only the noun broşür takes the locative ending. The adjective yeni stays the same.

This is very different from some European languages, but it is normal in Turkish.

üyelik bilgileri means something like membership information or membership details.

Here is the structure:

• üyelik = membership
• bilgi = information / a piece of information
• üyelik bilgisi = membership information
• üyelik bilgileri = membership information/details

In Turkish, plural bilgiler often means details or pieces of information, so üyelik bilgileri sounds very natural if there are several facts being given, such as:

• price
• requirements
• duration
• benefits

So English may use singular information, but Turkish often uses plural bilgiler / bilgileri.

This is a very common learner question, because -leri can look confusing.

In this sentence, üyelik bilgileri is best understood as a noun compound meaning membership details/information.

A few important points:

• üyelik bilgisi = membership information
• üyelik bilgileri = membership details / membership information

The ending here is not best understood as their information. It is part of a set expression-like noun phrase.

Why plural?

Because Turkish often uses plural on nouns like bilgi when talking about multiple items of information.

So even though English prefers information as an uncountable noun, Turkish may prefer a plural form that feels more like details.

Yes, literally yazıyor comes from yazmak = to write, and its basic form means is writing.

But Turkish also uses yazıyor idiomatically to mean:

• it says
• it is written
• it appears in writing

For example:

• Kapıda ne yazıyor? = What does it say on the door?
• Etikette fiyat yazıyor. = The price is written on the label.

So in your sentence, yazıyor does not mean that someone is physically writing at that moment. It means the information is there in written form.

This is very natural in everyday Turkish.

Yes, and the meaning changes slightly.

• yazıyor = it says / it is written there
  
  • very common and conversational
• yazılı = written, in written form
  
  • more descriptive, more static
• yazılmış = has been written
  
  • emphasizes that the writing was done

So you might also hear:

• Yeni broşürde üyelik bilgileri açıkça yazılı.
• Yeni broşürde üyelik bilgileri açıkça yazılmış.

Compared with those, yazıyor sounds a bit more like everyday it clearly says in the brochure.

Turkish often does not use a dummy subject like English it.

In English, you might say:

• It says clearly in the new brochure...

In Turkish, you can simply say:

• Yeni broşürde ... yazıyor.

The language does not need an explicit it here.

You can think of the sentence in two natural ways:

• The brochure says the membership details clearly
• The membership details are clearly written in the brochure

Turkish allows this kind of expression without adding a separate subject pronoun.

açıkça is an adverb meaning:

• clearly
• openly
• plainly

It describes how something is written.

So:

• açık = open / clear
• açıkça = clearly / openly

In this sentence:

• açıkça yazıyor = it is written clearly / it clearly says

This is a very common adverb form in Turkish.

Turkish word order is flexible, although some orders sound more neutral than others.

Your sentence:

• Yeni broşürde üyelik bilgileri açıkça yazıyor.

This is natural and neutral.

You could also hear:

• Üyelik bilgileri yeni broşürde açıkça yazıyor.
• Yeni broşürde açıkça üyelik bilgileri yazıyor.
  
  • possible, but less natural in many contexts

In Turkish, moving words around often changes focus rather than basic meaning.

The version you have puts the location first:

• In the new brochure, the membership information is clearly stated.

That is a very normal structure.

It is understandable and natural in everyday Turkish, especially because yazıyor is commonly used to mean it says / it is written.

However, some learners may first meet more textbook-like versions such as:

• Yeni broşürde üyelik bilgileri açıkça yazılı.
• Yeni broşürde üyelik bilgileri açıkça belirtiliyor.
• Yeni broşürde üyelik bilgileri açıkça verilmiş.

These can sound a little more formal or explicit.

So your sentence is fine, but it is useful to know that Turkish has several ways to express the same idea.