Forgiveness
The Order
Qur'an 3:103, 105
And hold fast, all of you together, to the Rope of Allāh (i.e. this Qur'ān), and be not divided among yourselves, and remember Allāh's Favour on you, for you were enemies one to another but He joined your hearts together, so that, by His Grace, you became brethren (in Islāmic Faith), and you were on the brink of a pit of Fire, and He saved you from it. Thus Allāh makes His Ayāt (proofs, evidences, verses, lessons, signs, revelations, etc.,) clear to you, that you may be guided.
...And be not as those who divided and differed among themselves after the clear proofs had come to them. It is they for whom there is an awful torment.
Hadith - Sahih Muslim (3/1340) and Ahmad (2/367)
The Prophet (sallallaahu alayhi wa sallam) said, Indeed Allah is pleased with three things: That you worship Allah alone without associating any partner along with Him; that you hold fast altogether to the Rope of Allah and not to become split-up; and that you give sincere advise to whomever Allah put in charge of your affairs.
The Noble Qur'an - An-Nur 24:22
And let not those among you who are blessed with graces and wealth swear not to give (any sort of help) to their kinsmen, Al-Masākīn (the poor), and those who left their homes for Allāh's Cause. Let them pardon and forgive. Do you not love that Allāh should forgive you? And Allāh is Oft-Forgiving, Most Merciful.
The Noble Qur'an - Al-'Imran 3:132-133
And obey Allāh and the Messenger (Muhammad SAW) that you may obtain mercy. And march forth in the way (which leads to) forgiveness from your Lord, and for Paradise as wide as are the heavens and the earth, prepared for Al-Muttaqūn (the pious - see V.2:2).
Allah's Great Mercy
Hadith - Qudsi 1
When Allah decreed the Creation He pledged Himself by writing in His book which is laid down with Him: My mercy prevails over my wrath.
Hadith - Qudsi 31
A man said: By Allah, Allah will not forgive So-and-so. At this Allah the Almighty said: Who is he who swears by Me that I will not forgive So-and-so? Verily I have forgiven So-and-so and have nullified your [own good] deeds (or as he said [it]).
Hadith - Qudsi 34
O son of Adam, so long as you call upon Me and ask of Me, I shall forgive you for what you have done, and I shall not mind. O son of Adam, were your sins to reach the clouds of the sky and were you then to ask forgiveness of Me, I would forgive you. O son of Adam, were you to come to Me with sins nearly as great as the earth and were you then to face Me, ascribing no partner to Me, I would bring you forgiveness nearly as great at it.
Hadith - Qudsi 20
The gates of Paradise will be opened on Mondays and on Thursdays, and every servant [of Allah] who associates nothing with Allah will be forgiven, except for the man who has a grudge against his brother. [About them] it will be said: Delay these two until they are reconciled; delay these two until they are reconciled.
The Noble Qur'an - 2:263
Kind words and forgiving of faults are better than Sadaqah (charity) followed by injury. And Allāh is Rich (Free of all wants) and He is Most-Forbearing.
Examples of Prophets asking for Forgiveness from Allah, swt
Mūsa (Moses)
The Noble Qur'an - 28:16
He said: "My Lord! Verily, I have wronged myself, so forgive me." Then He forgave him. Verily, He is the Oft-Forgiving, the Most Merciful.
The Noble Qur'an - 7:151
Mūsa (Moses) said: "O my Lord! Forgive me and my brother, and make us enter into Your Mercy, for you are the Most Merciful of those who show mercy."
Nūh (Noah)
The Noble Qur'an - 11:47
Nūh (Noah) said: "O my Lord! I seek refuge with You from asking You that of which I have no knowledge. And unless You forgive me and have Mercy on me, I would indeed be one of the losers."
The Noble Qur'an - 71:28
"My Lord! Forgive me, and my parents, and him who enters my home as a believer, and all the believing men and women. And to the Zālimūn (polytheists, wrong-doers, and disbelievers, etc.) grant You no increase but destruction!"
Sulaimān (Solomon)
The Noble Qur'an - 38:34, 35
And, indeed We did try Sulaimān (Solomon) and We placed on his throne Jasadan (a devil, so he lost his kingdom for a while) but he did return (to his throne and kingdom by the Grace of Allāh and he did return) to Allāh with obedience and in repentance.
He said: "My Lord! Forgive me, and bestow upon me a kingdom such as shall not belong to any other after me: Verily, You are the Bestower."
How to Ask for Forgiveness
Hadith - Bukhari 9.569, Narrated Abu Huraira
The Prophet (saaws) said, "None of you should say: 'O Allah! Forgive me if You wish,' or 'Bestow Your Mercy on me if You wish,' or 'Provide me with means of subsistence if You wish,' but he should be firm in his request, for Allah does what He will and nobody can force Him (to do anything)."
Hadith - Bukhari 1.796, Narrated Abu Huraira
I asked Allah's Apostle (saaws) to teach me an invocation so that I may invoke Allah with it in my prayer. He told me to say, "Allahumma inni zalumtu nafsi zulman kathiran, Wala yaghfirudhdhunuba illa anta faghfirli maghfiratan min 'Indika, war-hamni innaka antal-ghafururrahim (O Allah! I have done great injustice to myself and none except You forgives sins, so please forgive me and be Merciful to me as You are the Forgiver, the Merciful)."
Seek it how often?
Hadith - Sahih Muslim #6522, Narrated Al-Agharr al-Muzani
Allah's Apostle (peace be upon him) said: There is (at times) some sort of shade upon my heart, and I seek forgiveness from Allah a hundred times a day.
- Allah is the Forgiver of sins.