The month of Elul began on the evening of Aug. 26th.
“..the midrash…seems to characterize the entire month of Elul as…an opportune time and propitious opportunity in which Hashem’s presence is particularly accessible.” 
Asking forgiveness of others whom we might have hurt is often cited as one of the chief features of this month — preceding Rosh HaShanah and Yom Kippur. Yet, the other side of this — forgiving others — while certainly implied, is not cited as explicitly. In services I’ve led and conversations I’ve had, it has been the latter, more than the former, that people struggle with.
Can I forgive? Should I forgive? How do I forgive? And so on.
In preparing this post, I looked in my personal library and online for the specifics of how we can forgive. There is more than enough material if one looks — especially online. But that very abundance can seem daunting. There are so many different aspects to forgiving. So many different things that we seem to have to do.
Don’t think of “forgiving” as something you have to complete fully by Rosh HaShanah. Rather, “forgiving” is something we might have to learn to do; a skill we might have to master gradually. Some people forgive easily and slowly; some more slowly and with greater difficulty. Elul can be the time when we begin the process and take at least our first steps.
How can we begin?
We can do so by (at least) reading about forgiving. It’s often said that we forgive for our own benefit first. Anger, in the form of resentment or blame, etc., causes more discomfort to us than it does to the people who have hurt us. If we do no more during Elul than become sincerely convinced that we don’t want to prolong hurting ourselves — dayenu! I’d hope that reaching such a step would more or less automatically lead to asking: “How do I stop hurting myself?”
Most of the lists I looked at seem to imply that there’s a linear progression in how we go about forgiving. I don’t think that there is such a “line,” nor did the writers who compiled the lists necessarily think so, either. Forgiveness is a process that requires multiple steps, each of which you might do in no specific sequence; or — in a sequence that fits you personally. You might end up repeating steps, too. The process can resemble a “spiral” more than a line, as you move through the various levels of your own feelings and interpretations of the things that happened to you and the people who did them.
Here again, reading about forgiving can be part of both the beginning and the body of the process.
Parenthetically, reading about forgiving, even if not from Jewish sources alone, parallels “Torah study.” It involves “learning” and “doing.” “Learning” inspires and informs the “doing.” “Doing” culminates and fulfills the “learning.”
One feature of forgiving could perhaps be considered a “criterion” for where we’ve come in the process. That would be: Seeing yourself and the other person differently. We can’t change what happened, but we can change the way we view it, ourselves and the other.
“Forgiveness requires us to view our offender not as malevolent but as confused — so much so that they would actually believe that by harming us they could somehow become happier (though they would almost certainly be incapable of articulating that as the reason). Secondly, forgiving requires us to let go — of our anger; of our desire to punish or teach a lesson; of our need to harm our harmer; of the notion that by choosing to forgive an offense we’re in some way condoning an unjust action committed against us or committing an injustice ourselves; of the need for an apology; and of the need for our harmer to change. For in forgiving another their transgression against us, we’re ultimately seeking to free ourselves.” 
The Talmud says:
“All who overlook what’s owed to them, Heaven overlooks their sins in return.” 
One might say that the Talmud is noting that one who forgives is rewarded (so to speak) with a peace of mind far greater than revenge can provide.
We can begin by at least reading — becoming more informed — about why and how to forgive.
 Rosh HaShanah 17a