Difficulty: Moderately Easy
Step1
Meet with the person who also applied for the job ahead of time to be sure that she/he is the typ of person who will handle the situation well. Since you'll need to interact with them on a daily basis this is critical.
Step2
Once you are in the job, be friendly but not overly so; it won't come off as natural and they may feel you are only doing this to appease them.
Step3
Get to know them as a person and treat them with utmost respect.
Step4
Move slowly in making any suggestions or changes. If you are their boss or just a co-worker keep in mind if they've been there awhile you will need them to help orient you unless this is happening in some other fashion, such as through a special training program or through your boss.
Step5
Keep open communication. If things are unclear (or you think you've been told different things by your boss) go to your boss as a united front. Your co-worker will greatly appreciate your willingness to be a partner in working things out.
Step6
Give credit where credit is due. If your co-worker has been doing a fantastic job, then slip in some praise every once in a awhile particular if you are now his/her boss.