Dedenin anlattığı komik hikâye yüzünden torunlar uzun süre güldü.

It is one big noun phrase:

• dedenin = the grandfather’s / of the grandfather
• anlattığı = that he told
• komik hikâye = funny story

So the whole phrase means the funny story that the grandfather told.

A key difference from English is that Turkish puts the relative clause before the noun:

• [dedenin anlattığı] hikâye
  = the story [that the grandfather told]

Because it is the subject inside the relative clause, and in this kind of Turkish structure that subject usually takes the genitive ending.

• dede = grandfather
• dedenin = grandfather’s / of the grandfather

So in dedenin anlattığı hikâye, dedenin is the one doing the telling.

This pattern is very common:

• adamın yazdığı mektup = the letter that the man wrote
• öğretmenin verdiği ödev = the homework that the teacher gave

Anlattığı comes from the verb anlatmak = to tell.

Here it is not a normal finite verb like anlattı = he told. Instead, it is a relative-clause / participle form built with -DIK plus a possessive ending:

• anlat- = tell
• -tık / -dık / -dik / -duk type part = relative/nominal form
• -ı = 3rd person possessive/agreement ending

So anlattığı means roughly that he/she told.

You can compare:

• benim anlattığım hikâye = the story that I told
• senin anlattığın hikâye = the story that you told
• dedenin anlattığı hikâye = the story that grandfather told

The ending changes depending on who did the action.

Turkish usually does not use a separate relative pronoun like English that, which, or who.

Instead, Turkish makes a modifier from the verb and places it before the noun:

• English: the story that the grandfather told
• Turkish: dedenin anlattığı hikâye

So Turkish often expresses relative clauses by verb endings, not by an extra word.

Because the noun being described is left out inside the relative clause.

In dedenin anlattığı hikâye, the thing that was told is understood to be hikâye. Turkish does not repeat it with a pronoun like it.

So the logic is:

• dede ... anlattı = grandfather told ...
• what did he tell? hikâye
• that noun becomes the head noun outside the clause: dedenin anlattığı hikâye

This is very normal in Turkish relative clauses.

This is an important distinction.

• -an / -en is often used when the noun is the doer of the action.
• -DIK forms like anlattığı are often used when the noun is the thing affected by the action.

So:

• hikâyeyi anlatan dede = the grandfather who told the story
  Here dede is the doer.

• dedenin anlattığı hikâye = the story that the grandfather told
  Here hikâye is the thing told.

So anlatan and anlattığı are both correct forms, but they describe different nouns.

Yüzünden means because of, due to, or as a result of.

So:

• komik hikâye yüzünden = because of the funny story

A useful nuance: yüzünden often has a slightly negative or blaming tone in many contexts:

• Senin yüzünden geç kaldım = I was late because of you

But in everyday Turkish it can also be used more neutrally or playfully, as in this sentence. If you wanted a more neutral formal alternative, you might see:

• ... nedeniyle
• ... sebebiyle
• ... dolayı after the ablative

Turkish has no article system like English a/an/the.

So torunlar can mean:

• grandchildren
• the grandchildren

The exact meaning comes from context. In this sentence, English naturally translates it as the grandchildren.

Also, torunlar is the subject, so it does not take the accusative ending. If it were a direct object, the form could be different depending on definiteness.

Because Turkish very often uses a singular verb with a plural subject, especially when the subject is clearly stated.

So this is normal:

• Torunlar güldü = The grandchildren laughed

You may also hear:

• Torunlar güldüler

That is also possible, but with an explicit plural subject, the singular verb is very common and natural.

A simple way to think of it:

• if the subject is already there, Turkish often does not need extra plural marking on the verb.

Uzun süre means for a long time.

Literally, it is long duration / long period. Turkish often uses this kind of time expression without a preposition like English for.

So:

• uzun süre güldü = laughed for a long time

You could also say:

• uzun bir süre = a long time
• uzun süre boyunca = for a long time / throughout a long period

But uzun süre by itself is already very natural.

Not completely. Turkish word order is flexible, although the verb usually stays near the end in a neutral sentence.

This sentence is:

• Dedenin anlattığı komik hikâye yüzünden torunlar uzun süre güldü.

A very natural alternative is:

• Torunlar dedenin anlattığı komik hikâye yüzünden uzun süre güldü.

Both are fine. The difference is mostly about focus and emphasis.

Starting with dedenin anlattığı komik hikâye yüzünden puts the cause in a prominent position:

• Because of the funny story the grandfather told, the grandchildren laughed for a long time.

So Turkish often moves pieces around to highlight what feels most important.