We can forgive the sins of those who sin against us, basically by wiping the slate clean for that person and asking God not to hold it against them on our account.
I'd like to expand on that one just a bit because it falls into one of those areas that is widely misunderstood. God asks us to forgive not because He needs us to do that before He can forgive, but because it's good for us (practically and developmentally) and good for the building up of the community (in practical terms). And because when we try to approximate His way of seeing things, we tend to see them and respond to them differently that we would tend to react from our own, narrower view.
And there again is an area where believers and non-believers have a value in common-- "the greatest good."