In the Name of Allah, most Compassionate, most Merciful

Da'wah is invitation to deen and the right path and applies on any non believer.  In this case Prophet Muhammad (S) was instructed to do da'wah to the pagans of Makkah.  The believers themselves use to get together and learn the Quran and Sunnah with Prophet Muhammad (S).  This pattern continued in Madinah as well.  There were gradual changes to this pattern as the life went on in Madinah.  His (S) position became more global and sent letters to all the rulers or the people of power in the empires of his time.  Prophet Muhammad (S) was also ordered to fight any aggression from disbelievers while living in Madinah.

Things started to change dramatically towards the end of Prophet Muhammad's (S) life as he had a small army and he was able to take it to the tribes of Arabia and invite people to Islam.  This was the case because most of the tribes in Arabia would help the Romans or Persians against Muslims.  Sooner Prophet Muhammad (S) would fight all the tribes specially after the following verses were revealed:

Quran 9:1. Freedom from all obligations (is declared) from Allah and His Messenger (SAW) to those of the disbelievers, with whom you made a treaty.  

9:5. Then when the Sacred Months have passed, then kill the disbelievers wherever you find them, and capture them and besiege them, and prepare for them each and every ambush. But if they repent and perform As-Salat , and give Zakat, then leave their way free. Verily, Allah is Oft-Forgiving, Most Merciful.  

9:6. And if anyone of the disbelievers seeks your protection then grant him protection, so that he may hear the Word of Allah, and then escort him to where he can be secure, that is because they are men who know not. 

So towards the end of his life, he took his armies to people with three conditions, become Muslim, pay Jizyah, or fight to death.  Now this mission did not only apply to the tribes helping the Romans/Persians against the Muslims but any non believer tribes anywhere, even outside of Arabia.  The only people spared were the ones who came only to learn the deen and hear about Islam and go back to their people.

Quran 9:29. Fight against those who believe not in Allah, nor in the Last Day, nor forbid that which has been forbidden by Allah and His Messenger and those who acknowledge not the religion of truth even the people of the Scripture, until they pay the Jizyah with willing submission, and feel themselves subdued. 

So the last phase of Da'wah applied for those disbelievers in any part of the world who would willingly want to learn about Islam and they had to come to the Muslims.  The Muslims did not go out like 'missionaries' but only to conquer lands and establish Shariah.  Eventually after Prophet's (S) death, the Sahabas continued to expand Islam and send the armies all over the world and thus fulfil their covenant with Allah as stated in the above verses.  The believer armies would only go with the three conditions, either surrender and pay Jizyah, fight to death or become Muslim.  While all this happened, any person who would become Muslim was made obligatory to learn the deen and Quran from his ability.  Islam became powerful through the sword.

Now a days, the so called Muslims have changed all this and they apply their own rules of Da'wah and Tabligh.  They do not learn and follow the Quran, Sunnah and Sahabas anymore.  They leave the hypocrites and disbelievers alone and rely only on Da'wah and words of mouth like missionaries.  And this is not commanded by Allah anymore because of Surah Touba.  

None of Our revelations do We abrogate or cause to be forgotten but We substitute something better or similar; know you not that Allah has power over all things? [Surah 2:106]

The Da'wah verses of Makkah were abrogated with something better but people still follow them in disobedience or ignorance of Quran.

Sahih Muslim Hadith 32 Narrated by Jabir ibn Abdullah
Allah's Apostle (peace be upon him) said: I have been commanded that I should fight against people till they declare that there is no god but Allah, and when they profess it that there is no god but Allah, their blood and riches are guaranteed protection on my behalf except where it is justified by law, and their affairs rest with Allah, and then he (the Prophet) recited (this verse of the Qur'an): 'Thou art not over them a warden.

The next hadith explains that not only to fight disbelievers but hypocrites as well.

Sahih Al-Bukhari Hadith 2.483 Narrated by Abu Huraira
When Allah's Apostle died and Abu Bakr became the caliph some Arabs renegade (reverted to disbelief) (Abu Bakr decided to declare war against them), 'Umar, said to Abu Bakr, "How can you fight with these people although Allah's Apostle said, 'I have been ordered (by Allah) to fight the people till they say: "None has the right to be worshipped but Allah, and whoever said it then he will save his life and property from me except on trespassing the law (rights and conditions for which he will be punished justly), and his accounts will be with Allah.' " Abu Bakr said, "By Allah! I will fight those who differentiate between the prayer and the Zakat as Zakat is the compulsory right to be taken from the property (according to Allah's orders). By Allah! If they refuse to pay me even a she-kid which they used to pay at the time of Allah's Apostle . I would fight with them for withholding it" Then 'Umar said, "By Allah, it was nothing, but Allah opened Abu Bakr's chest towards the decision (to fight) and I came to know that his decision was right."