Though breaking up a couple is a dangerous endeavor, if you think you really belong with a person who is dating someone else, then it's worth giving it a shot. To break up a couple, you have to proceed with caution by first planting the seeds of doubt before making the break-up inevitable.
The worst thing you can do is openly criticize the person's relationship, criticize the person's partner, or generally make the person feel like he or she is in a doomed relationship. This will make the person feel angry, defensive, and more determined than ever to make things work. No one wants to admit to a failure, especially not in a relationship, so you have to wait for the person to naturally admit a problem on his or her own.