In business, like the rest of life we will often encounter people who are just that little more difficult to get along with. Some use the term "personality conflict" to describe the situation, yet this suggests that there is some sort of unbreakable barrier and that the problem is somewhat unfixable, since it is highly unlikely somebody is going to change their entire personality for the sake of better work relations!
Situations with difficult employees tend to occur over time; after all it is not very common to hire someone and find them impossible to deal with after the first week. Usually it is small irritating personal habits that progress over time into larger annoying behaviours after being left unattended. In any relationship, both people influence the other's behaviour. In almost every conflict situation, both parties bear some responsibility for the way things end up.
Focusing on blame will produce no results and only irritate you further. The most proactive thing you can do in these situations is focus on what YOU can do to make things better. It doesn't matter who is at fault, if your primary concern is to rectify the situation. Try to consider your contribution in this unpleasant situation; perhaps you have just written them off as a lost cause, their own worst enemy? Now try to consider ways in which you can change this; maybe by getting more involved with them personally, making an effort to become friends.
A good idea is to approach the situation in a non- accusatory tone, preferably when you are both calm and in a private situation. Address the problems you are experiencing, once you have finished let them have their say and be sure to listen intently so they know you are truly concerned and interested. When possible find things to agree on, and offer something in return.
If you are clearly frustrated it will show. It is important that you deal with things firmly, but nicely and without dramatics. To remain the bigger person you should retain quiet dignity, even if the other person becomes rude or nasty. No-one is suggesting you smile and turn the other cheek in the face of abuse, but if you counter-attack or react in kind, you will almost always make the situation worse.
Avoid gossip of any kind as you will start to involve other members of staff. As well as being disruptive to the organization, it will make it more difficult to fix the situation. Gossip only focuses on the worst part of a person and paints them in a very negative light. Along with being unfair, it affects your thinking and actually shortens your patience, especially when you get covert support from others.
Like every situation, prevention is better than cure, by using a combination of politeness and limit setting these situations can be completely avoided. However, sometimes the conflict becomes so polarized that you will have to go to outside sources to seek help. If the person in question is a fellow staff member, one possibility is to approach your team leader and explain the situation. Do your best not to convince your boss how "bad" the other person is, it will just make you look like the problem.
At the end of the day there is generally a solution to every problem. If the situation persists and you and the person in question continue not to see eye to eye, then perhaps mediation or some other form of intervention may be necessary. In any case you must remember that there are two sides to every story, maybe you aren't being as reasonable as you originally thought? Be open to others suggestions and opinions, and be aware of your rights and responsibilities in a conflict situation, as well as theirs.