In Sha' Allah
In sha' Allah (also written as inshallah or insha'Allah), in Arabic إن شاء الله, is an Islamic phrase used not only by Arab Muslims, but also by English-speaking Muslims. The literal meaning of "in sha' Allah" is "if wills God" and Muslims have to (because of verses 18:23-24) say this phrase whenever they say their plan to do something.
The phrase in Arabic
With diacritics it is written as:
- إِن شَاءَ اللَّهُ
In the old Qur'anic Uthmani script, the شَاءَ is written with alif maddah:
- إِن شَآءَ ٱللَّهُ
The three words are:
- إِن - in - (a particle) if
- شَاءَ - sha' - (3rd person perfect verb) wills 
- اللَّهُ - Allah - (proper noun) God
The three letters in شَاءَ are:
- ش - shin
- ا - alif
- ء - hamza
Hamza is read as a glottal stop (closing the throat), which is indicated by the apostrophe "In sha' Allah".
The root of شَاءَ is شيا.
Some Muslims write in and sha together, so they get insha. انشاء الله (insha' Allah) means "we created/invented Allah" (insha is from a different root نشا). So by writing in and sha' together they proclaim that Allah is a man-made god. 
In the Qur'an
The verses 18:23-24 are the most important since they command Muslims to say in sha Allah. The verse 18:24 actually says أَن يَشَآءَ ٱللَّهُ (an yasha' Allah) and not ان شاء الله (in sha' allah):
18:23 And never say of anything, "Indeed, I will do that tomorrow,"18:24 Except [when adding], "If Allah wills." (أَن يَشَآءَ ٱللَّهُ) And remember your Lord when you forget [it] and say, "Perhaps my Lord will guide me to what is nearer than this to right conduct."
These verses say in sha Allah. Shakir translates the phrase as "if Allah pleases":
In the Qur'an sometimes it is also written as "law sha Allah" (لَوْ شَآءَ ٱللَّهُ):
In the hadith
Oaths with in sha' Allah are unbreakable:
Muhammad's religious tolerance:
Solomon's wives didn't get pregnant, because he didn't say in sha' Allah:
In Ibn Ishaq's sira (biography of Muhammad), we can read that some people were sent to Jewish rabbis, to ask them how to determine whether Muhammad is a real prophet. They prepared 3 questions for Muhammad and if he answers them right, then he is a prophet. Muhammad said, he will give them the answers tommorow, but after 15 days he was still without any answers. Supposedly because he didn't say "in sha' Allah":
They came to the apostle and called upon him to answer these questions. He said to them, 'I will give you your answer tomorrow,' but he did not say, 'if God will.' So they went away; and the apostle, so they say, waited for fifteen days without a revelation from God on the matter, nor did Gabriel come to him, so that the people of Mecca began to spread evil reports, saying, 'Muhammad promised us an answer on the morrow, and today is the fifteenth day we have remained without an answer.' This delay caused the apostle great sorrow, until Gabriel brought him the Chapter of The Cave, in which he reproaches him for his sadness, and told him the answers of their questions, the youths, the mighty traveller, and the spirit.I was told that the apostle said to Gabriel when he came, 'You have shut yourself off from me, Gabriel, so that I became apprehensive'. He answered, 'We descend only by God's command, whose is what lies before us, behind us, and what lies between, and thy Lord does not forget.
The last sentence by Gabriel became a verse in the Qur'an:
After 15 days Muhammad revealed vague answers to the questions. The revealed answers seem to be collected from rumors of the people and not from an all-knowing being, because they include phrases like "some people say" with a list of different rumors, instead of giving the exact number. They also include the "Allah knows best" excuse. This verse deals with the number of the sleepers of Ephesus:
Immediately after that verse (18:22), come the verses (18:23-24) about the necessity of saying in sha' Allah:
18:23 And never say of anything, "Indeed, I will do that tomorrow,"
18:24 Except [when adding], "If Allah wills." (أَن يَشَآءَ ٱللَّهُ) And remember your Lord when you forget [it] and say, "Perhaps my Lord will guide me to what is nearer than this to right conduct."
So if Islam is true, then Allah refused to help Muhammad with his challenge to prove his prophethood, just because Muhammad didn't say in sha' Allah. But somehow after 15 days he helped him anyway. Also Allah's knowledge seems to be limited by the knowledge of people around Muhammad, because instead of giving the exact number of the sleepers of Ephesus, he gave an answer like "some people say this and some people say that".
And if Islam is false, than it means that Muhammad probably didn't have the answers to the questions and hoped someone would help him with it until the next day, but eventually it took him 15 days to collect at least some vague answers and then as an excuse for his delay he said that it was because he didn't say in sha' Allah.
Saying in sha' Allah is supposed to help people achieve their goals/wishes. If people don't say in sha' Allah, then their goals shouldn't be achieved (for example, Solomon couldn't have kids without saying in sha' Allah). But since people from other religions and atheists can achieve their goals without saying in sha' Allah and Muslims do not always achieve their goals despite saying in sha' Allah, then the effectiveness of this phrase on achieving goals is approximately 0%.
- Insha is used in the Qur'an. For example in 23:78:
- وَهُوَ ٱلَّذِىٓ أَنشَأَ لَكُمُ
- It is whe who created (أَنشَأَ) for you