How to forgive in a modern world?

As a practicing Catholic, I know that God tells us to forgive (Luke 17:4 esp.) but how can we do that in a modern world? If we forgive those who have hurt us, are we just making doormats of ourselves and not really giving ourselves any respect? In my situation that has got me thinking about this, how can I forgive a backstabbing close friend, if I'm no where near convinced she won't do it again? In a modern world, with so many hurtful people, how can we forgive?