HIDAYAH OR GUIDANCE
Hidayah or Guidance means guiding someone to the true and right path. 
Qur’an is a Book of guidance, Qur’an.Surah Baqarah 2:185, revealed by Allah (Glory be to Him) for all mankind from the time of Prophet Muhammad (May Allah honour Him and Grant Him peace) to the end of this world.
Guidance is in the hand of Allah (Glory be to Him) alone. The Messenger of Allah (May Allah honour Him and Grant Him peace) has no part in guidance; all that he and the Muslims have to do is to explain and convey the message, but they cannot force people to follow it, as Allah (Glory be to Him) said to His Messenger (May Allah honour Him and Grant Him peace) (interpretation of the meaning): “And had your Lord willed, those on earth would have believed, all of them together. So, will you (O Muhammad) then compel mankind, until they become believers” Qur’an.Surah Yunus 10:99
And Allah (Glory be to Him) says (interpretation of the meaning): “And the duty of the Messenger is only to convey (the Message) plainly” Qur’an.Surah Ankabut 29:18
Allah (Glory be to Him) guides whomsoever He wills and sends astray whomsoever He wills. He guides those who obey Him and turn to Him, as He says (interpretation of the meaning): “While as for those who accept guidance, He increases their guidance and bestows on them their piety” Qur’an.Surah Muhammad 47:17
But whoever disobeys Allah (Glory be to Him) and turns away from Him, Allah (Glory be to Him) will not guide him, as He says (interpretation of the meaning): “Truly, Allah guides not him who is a liar, and a disbeliever” Qur’an.Surah Zumar 39:3 
Islam is the religion of the natural state of man (fitrah), the religion of reason and thought. Allah (Glory be to Him) has distinguished the truth from falsehood. He has enjoined all that is good and forbidden all that is evil. He has permitted good things and forbidden evil things. There is no compulsion in religion because the benefits or harms come back upon the created being, not upon the Creator. Allah (Glory be to Him) says (interpretation of the meaning): “There is no compulsion in religion. Verily, the Right Path has become distinct from the wrong path. Whoever disbelieves in Taaghoot (false gods or dities) and believes in Allah, then he has grasped the most trustworthy handhold that will never break”Qur’an.Surah Baqarah 2:256
Man has the choice in terms of his reason only; if he loses his reason by which he is able to distinguish between the alternatives of good and evil, truth and falsehood, then he is not accountable. Hence according to Islamic shariah, the pen is lifted from the insane person (i.e., he is not accountable) until he recovers his senses, and from the child until he reaches the age of understanding, and from the sleeper until he wakes up. None of these people are accountable until they gain or recover the reason by which they may distinguish between the alternatives of faith and disbelief, truth and falsehood, and so on.
Allah (Glory be to Him) has created man and given him reason, and He has sent down to him Revelation and sent to him Messengers to call him to the truth and warn him against falsehood. Then He has left him to make his own choice. “And say: ‘The truth is from your Lord.’ Then whosoever wills, let him believe; and whosoever wills, let him disbelieve”Qur’an.Surah Kahf 18:29  
Muslims ask Allah (Glory be to Him) for His guidance every day, in each prayer. In surah Fatiha, a surah which is compulsory for every Muslim to read in his/her salat, it is said: "guide us to the straight path".
It is a Sunnah to pray Allah (Glory be to Him) for guidance of a disbeliever. The best thing to is to pray for guidance for that person. As is reported in a number of Hadith, such as the following:
Abu Hurayrah® reported that Tufayl ibn ‘Amr ad-Dausi and his companions came to the Prophet Muhammad (May Allah honour Him and Grant Him peace) and said: “O Messenger of Allah, Daus have rebelled and disobeyed, so pray to Allah against them.” People said, “Now Daus are doomed!” He said, “O Allah, guide Daus and bring them here.” Sahih Al Bukhari, Vol 4:188
Abu Hurayrah (R) said: “I was calling my mother to Islam, when she was still a mushrik. One day I called her to Islam and she said something about the Messenger of Allah (May Allah honour Him and Grant Him peace) that upset me. I came to the Messenger of Allah (May Allah honour Him and Grant Him peace), weeping, and said: ‘O Messenger of Allah, I was calling my mother to Islam and she refused. Today I called her and she said something about you that upset me. Pray to Allah to guide the mother of Abu Hurayrah®.’ So the Messenger of Allah (May Allah honour Him and Grant Him peace) said: ‘O Allah, guide the mother of Abu Hurayrah ®.’ I left, feeling hopeful because of the Prophet’s prayer. When I got home, as I came near to the door I saw it was ajar. My mother heard my footsteps and said, ‘Stay where you are, Abu Hurayrah®!’ I could hear the sound of water. She washed herself, got dressed and put on her khimaar (head covering). Then she opened the door and said, ‘O Abu Hurayrah®, I bear witness that there is no god except Allah, and I bear witness that Muhammad is His slave and Messenger.’ I went back to the Messenger of Allah (May Allah honour Him and Grant Him peace), weeping with joy, and said, ‘O Messenger of Allah, good news! Allah has answered your prayer and has guided the mother of Abu Hurayrah®.’ He praised and thanked Allah (Glory be to Him), and said, ‘That is good.’ I said, ‘O Messenger of Allah, pray to Allah to make my mother and me dear to His believing slaves, and to make them dear to us.’ The Messenger of Allah (May Allah honour Him and Grant Him peace) said, ‘O Allah, make this slave of Yours (meaning Abu Hurayrah) and his mother dear to Your believing slaves, and make the believers dear to them.’ There is no believer who hears of me or sees me, but he loves me.”Sahih Al Muslim 6082.
Jaabir(R) said: “They said, ‘O Messenger of Allah, we have suffered much from the arrows of Thaqeef (this was when they were fighting, before they became Muslim), so pray to Allah against them.’ He said, ‘O Allah, guide Thaqeef.’” Al-Tirmidhi, who said: this is a hasan sahih ghareeb hadith. Sunan Al-Tirmidhi 3877.