When should I use the 是...的 construction?
The answer is a modified citation of this awesome article: The 是 … 的 construction in Mandarin, credit of original article goes to Hugh Grigg (eastasiastudent.net). There are more links around this subject at the bottom of the original article.

That article and this answer are published under Creative Commons license CC BY-NC-SA 3.0.

Note not everything with 是 and 的 is a '是 … 的 construction'. This answer speaks specifically to '是 … 的 construction' as that's what the question is about.



The 是 … 的 construction in Mandarin grammar is very useful to know. It’s used to emphasize a particular detail in a sentence.

The 是 … 的 construction picks out one of the following kinds of information:


time
manner
place


The structure is common and pretty easy to use and understand.

Forming a 是 … 的 sentence

是 is placed right before the piece of information you want to draw attention to, and 的 comes at the end of the sentence. Whatever comes immediately after 是 is emphasized. This is equivalent to saying “It was … that …” in English (although English often just uses tone of voice to emphasis).

Examples:


  她是昨天去的。Tā shì zuótiān qù de. It was yesterday that she went.
  
  我是跟我朋友出去的。Wǒ shì gēn wǒ péngyǒu chūqù de. It was my friends who I went out with.
  
  我是在北京学习中文的。Wǒ shì zài běijīng xuéxí zhōngwén de. It was in Beijing where I studied Chinese.


Emphasizing different parts of the sentence

是 can be placed at any one of three points in a sentence to draw attention to what comes after it. In the following sentence, for example,


  我上个星期五跟我女朋友在饭馆吃饭。Wǒ shàng gè xīngqíwǔ gēn wǒ nǚ péngyǒu zài fànguǎn chīfàn. Last Friday I ate dinner with my girlfriend in a restaurant.


Time, manner or place could be picked out with 是 … 的.


  我是上个星期五跟我女朋友在饭馆吃饭的。
  
  Wǒ shì shàng gè xīngqíwǔ gēn wǒ nǚ péngyǒu zài fànguǎn chīfàn de.
  
  It was last Friday that I ate dinner with my girlfriend in a restaurant.
  
  我上个星期五是跟我女朋友在饭馆吃饭的。
  
  Wǒ shàng gè xīngqí wǔ shì gēn wǒ nǚ péngyǒu zài fànguǎn chīfàn de.
  
  It was with my girlfriend that I ate dinner in a restaurant last Friday.
  
  我上个星期五跟我女朋友是在饭馆吃饭的。
  
  Wǒ shàng gè xīngqí wǔ gēn wǒ nǚ péngyǒu shì zài fànguǎn chīfàn de.
  
  It was in a restaurant that I ate dinner last Friday with my girlfriend.


Note how in English this involves rearranging all the elements of the sentence, but in Chinese their position is fixed. All that’s needed is to place 是 in front of the part to be emphasized, and 的 at the end of the sentence.

What you can emphasize with 是 … 的

Broadly speaking, the 是 … 的 construction emphasizes time, manner or place. This covers a lot of uses though. Here are some examples:


  我今天是开车上班的。
  Wǒ jīntiān shì kāichē shàngbān de.
  Today I came to work by car.
  
  我是用法文写这封信的。
  Wǒ shì yòng fǎwén xiě zhè fēng xìn de.
  I wrote this letter in French.
  
  他是在网上发现这个信息的。
  Tā shì zài wǎngshàng fāxiàn zhège xìnxī de.
  He found out this information online.
  
  那个故事是我爷爷告诉我的。
  Nàgè gùshì shì wǒ yéye gàosu wǒ de.
  It was my grandfather that told me that story.
  
  他是对我感兴趣的。
  Tā shì duì wǒ gǎn xìngqù de.
  He was interested in me.


You can draw attention to pretty much any information in the sentence using 是 … 的.

Forming questions with 是 … 的

You can also form questions with the 是 … 的 construction. This is done in the usual ways to form questions:


With 吗
With a question word
With verb / negative inversion


Examples:


  你那天是去伦敦的吗？
  Nǐ nèitiān shì qù lúndūn de ma?
  Did you go to London that day?
  
  他是给谁打电话的？
  Tā shì gěi shéi dǎ diànhuà de?
  Who was it that he phoned?
  
  我是不是五月出生的？
  Wǒ shì bù shì wǔ yuè chūshēng de?
  Was it in May that I was born?


Note that with the 吗 question, 吗 comes at the end of the sentence as usual, with 的 just before it (this is probably what you were expecting anyway).

The negative form of 是 … 的

是 … 的 is negated as you would expect, with 不. This is used to draw attention to the fact that something is not the case.

Examples:


  我们不是在巴黎认识的。
  Wǒmen búshì zài bālí rènshi de.
  It wasn’t in Paris that we met.
  
  我的钱包不是被他偷走的。
  Wǒ de qiánbāo búshì bèi tā tōu zǒu de.
  My wallet wasn’t stolen by him.


是 … 的 implies completion

Because 是 … 的 emphasizes the details around an action, there is an implication that the action has been completed (so that we can know the details). However, this is just an implication, and not the main function of this construction. 是 … 的 is used to draw attention to extra details of an action, not to indicate its completion. 了 should be used to mark completion.

Moving 的

Normally, 的 is placed at the end of the sentence in a 是 … 的 construction, and this is fine most of the time. However, it can also be placed before the object. The only time this is necessary is when the 是 … 的 construction would result in a sentence with another meaning to the one intended. For example:


  我是在网上卖衣服的。 Wǒ shì zài wǎngshàng mài yīfu de. I sell clothing online.


Rather than emphasizing that the clothes are sold online, this sentence ends up saying that the speaker is some sort of online clothing merchant. To avoid this misinterpretation, 的 can be placed before the object:


  我是在网上卖的衣服。 Wǒ shì zài wǎngshàng mài de yīfú. It was online that I sold
  the clothes.


Now the sentence has the intended meaning (that the speaker sold some clothes on Taobao or something). The sentence above about studying in Beijing is actually ambiguous for this reason:


  我是在北京学习中文的。 Wǒ shì zài běijīng xuéxí zhōngwén de. I studied Chinese in Beijing.


This could just as well be translated as “I am a Chinese learner in Beijing”, with no emphasis, in which case 的 functions as a particle that converts verb phrase (study Chinese) into attributive (Chinese studying (person)). To avoid this, 的 can be placed in front of the object:


  我是在北京学习的中文。 Wǒ shì zài běijīng xuéxí de zhōngwén. It was in Beijing
  that I studied Chinese.


Now the emphasis is clear.

This situation only comes up occasionally though, so most of the time it's fine to put 的 at the end of the sentence (although you often see it placed before the object anyway).

Omitting 是

One final thing to note is that sometimes 是 can actually be omitted and the structure is still valid. This can't happen all the time, though. If the subject is a demonstrative pronoun (这 or 那), you have to include 是. If the sentence is negative, you also need 是 (it would sound pretty strange without it). Otherwise, 是 can generally be omitted and the sentence is still valid.

If the sentence is complicated with many parts (e.g. time, manner and place) then 是 will need to be inserted to clarify what’s being emphasized.

Not everything with 是 and 的 is a 是 … 的 construction!

Remember that just because a sentence uses 是 and 的 doesn’t mean it’s emphasizing something. Far from it, in fact. 是 and 的 are a very common way to attach attributes to things. For example:


  这辆车是红色的。 Zhè liàng chē shì hóngsè de. This car is red.


The sentence above is not a 是 … 的 construction as described in this article. It's just a bog-standard descriptive sentence. The 是 … 的 construction emphasizes additional information about an action rather than just modifying things.

Summary


是 is placed before the part of the sentence you want to emphasize.
的 is nearly always placed at the end of the sentence. Sometimes it appears before the object.
All the usual question formations can be applied to 是 … 的 sentences.
是 … 的 is negated with 不.
是 … 的 implies completion of the action, but shouldn't be used to express this specifically.
是 can be omitted in some circumstances.