It is related from our Prophet (s.a.w) that he said about Ramadan, “Its beginning is mercy, its middle is forgiveness, and its ending is liberation from the Hellfire.” The stage of mercy has come and gone; now is the time for forgiveness. The mercy of God surrounds us as a manifestation of his name Rahman, whether we want to or not, whether we deserve it or not. (His name Rahim, however, is more about worthiness.)
As for forgiveness, which means the covering of our mistakes- since it is commanded to us in countless places in the Quran to seek Allah’s (s.w.t) forgiveness, becoming a recipient of God’s forgiveness is largely a matter of our demand and seeking it out. As al-Ghazali points out, just as God covers our internal organs and our bodies with the most beautiful covers, he covers our ugliest and most unspeakable mistakes and sins with his vast forgiveness.
According to what we learn from the Quran and the sunnah, whatever we want from our Lord, we first have to bring it into being in our own character and conduct (of course by using what God has bestowed upon us in the first place). This is to say, whoever wants forgiveness should be forgiving; whoever wants mercy should be merciful; whoever wants generosity should be generous, etc. However we want Allah (s.w.t) to treat us on Judgment Day, we should treat our fellow human beings the same way.
If I had more space I would briefly touch on the rewards promised to those who pray for forgiveness, as told in verses 10-12 of Surah Nuh, but I will have to content myself with encouraging you to look these verses up yourselves.