What is the way of establishing peace with non-Muslims? What are the conditions of doing that?

Islam has brought universal basis. It is possible to see that in the verses related with peace, (Believers:) make ready against them whatever you can of force and horses assigned (for war) (Al-Anfal Surah, 8:60) but in the following verse it is stated as, And if they (the enemies) incline to peace, incline to it also, and put your trust in God. Surely, He is the All-Hearing, the All-Knowing. For peace is the main purpose, not the war.

Muslims should reach to the ultimate power. However, it should not be used to annihilate the enemies rather should be used to deter them. If the enemy inclines to peace, Muslims must incline to it too. Just because the occasion arises, to annihilate them all has never been approved.

Peace that is ordered by the verse is a valuable one. Otherwise, seeking peace in contempt is not an action that fits to a Muslim. So (when in warfare with the enemy) do not be faint of heart and cry out for peace (which will bring you humiliation) when you have the upper hand. (Always bear in mind that) God is with you, and He will never diminish the reward of your good deeds. (Muhammad Surah, 47:35) As Late Hamdi Yazir puts it, it is not a matter of rejecting to the peace or not but accepting it faint-heartedly which will bring humiliation. (2)

Considering only verses that order war, and disregarding the ones, which encourage peace, is nothing but not knowing Islam completely. Some Muslims fall into the same error as Western researchers does, and claim that, Islam has spread by sword. In order not to fall into such errors, one should not avoid comprehending Quranic verses. The Surah Al-Mumtahana, which was revealed before the conquest of Mecca, brings this pleasant news to the believers: (When you obey God in His commands and prohibitions), it may be that God will bring about love and friendship between you and those of them with whom you are in enmity, God is All-Powerful, and God is All-Forgiving, All-Compassionate. God does not forbid you, as regards those who do not make war against you on account of your Religion, nor drive you away from your homes, to be kindly to them, and act towards them with equity. God surely loves the scrupulously equitable, God only forbids you, as regards those who make war against you on account of your Religion and drive you away from your homes, or support others to drive you away, to take them for friends and guardians. Whoever takes them for friends and guardians, those are the wrongdoers. (Al-Mumtahana Surah, 13:7-9)

As it is seen, it is made a clear distinction between atrocious enemies of religion and those who are not, in these verses. In the first verse, it is indicated the possibility of providing peace between Meccan disbelievers and Muslims. By the conquest of Mecca, the love that was promised by God became true, Disbelievers reverted to Islam, and they all became brothers.

Sources:
1-Yazır, IV, 2425
2-Yazır, VI, 4398
3-Beydavi, II, 486-487
4-Razi, XXIX, 303