Dealing with a difficult coworker is frustrating and draining. You don't have any control over whom you work with, and an annoying co-worker can impact your mood, hurt your productivity and taint your immediate work environment. If you're dealing with a co-worker you can't stand, you'll need to make some adjustments to your routine and behavior at work to minimize the negative impact on you. You can't change your co-worker, but you can alter the way you're approaching the situation.
Examine the Situation
Confirm that your dislike of your co-worker is coming from a rational place and is unlikely to fade anytime soon. For example, if you can't stand a colleague in your office because she is incredibly rude to you, your dislike is justifiable. But if you don't really know much about her and hate her because of stories you've heard or some very limited interaction, try getting to know her yourself. You may find your hatred lessening and even disappearing entirely once you know her better and understand where she's coming from.
If you've tried to overcome your hatred of your co-worker but can't, acknowledge where the problem lies and what you're feeling. Recognize that her hurtful behavior toward you is a failing on her part -- and not your fault -- to minimize its effect on you. While you're only human and will feel some anger or hurt from your co-worker's behavior toward you, reminding yourself it's her problem will help you handle her in a polite way.
Limit your contact with the co-worker as much as possible. It's easier to remain civil toward a co-colleague you dislike if you don't have to constantly interact with her. Don't engage her in conversations or participate if she tries to engage you in one. Keep any necessary conversations with her limited to the job or task at hand only. This will ensure you'll get the work done while keeping the talking brief. Use electronic or remote communication, such as the telephone and email, whenever possible.
People often respond in kind to tone of voice, body language and other subconscious cues when they're talking to another person. If you're polite in tone and words and keep your body language neutral and formal, your co-worker is likely to respond in kind, making it easier for you to behave civilly. Don't bring emotions into it and try to keep yourself from acting in a patronizing manner.
Know Your Limit
Speak to your supervisor if your co-worker is behaving in an abusive manner toward you. An annoying, gossip or rude co-worker is someone you'll have to handle, but you shouldn't put up with a colleague who is threatening you or being verbally abusive. In cases of abuse, you'll have to ask your boss or human resources department to step in. Document the abuse for your superiors by writing down instances and keeping copies of electronic communications. Ask other staff who have witnessed your co-worker's behavior for statements.