It's easier to forgive if something was in the past and isn't still happening. If it still is, I guess the best thing to do is separate yourself from that person or whatever it is they're doing, if possible.
I tend not to make my annoyances public (such as I don't tell the person or others about it) so generally I just forgive them mentally and just try to forget about it if it's someone that I don't interact with anymore. But I do try to learn from it and avoid the situation or whatever in the future, so it doesn't happen again.
I think forgiveness is important because if you don't forgive, then the pent up anger or stress causes more harm. :/
Underneath the cold November sky, I wait for you... As the pages of my life roll by, I wait for you... I'm so desperate just to see your face, meet me in this broken place...
Be a little brave for a little bit of time.