I am talking about a personality conflict, between two people or more, that builts up tension in the team, ruins the team spirit and worsen the quality of life at work. Most of the time, those are not open conflicts, but unspoken; but you can sometime feel the heat. How to deal with those kinds of situations before they get worse. Do you apply a process or do you have a personal way to solve interpersonal conflicts? What works the best? I am talking about a situation where everybody suffer about it in the team.
Since we are dealing with people the combination of issues that can arise are endless. As such it's really hard to answer without some context.
While every business/team is unique and all our operating environments are different, I think that in general the following will often apply:
Management is a continuous effort. Most teams like to keep it within themselves so if you so much as get a whiff of something that smells bad, start digging. Ideally it is you who goes down to the team level and start the tweaking before it even gets to your level through the normal protocol. That way you can nip it in the bud. When issues get brought up to you through the normal chain of command, its often reached a stage where resolution is hard or even impossible and egos will often be bruised.
It's not just two people. When interpersonal issues come up, the entire team is affected. There will be whining and venting on a member to member level so odds are the other people will have taken sides in the issue as well. You need to make sure you weigh the impact of your decisions before you make a stand. Having to keep the team in mind means you may not always end up making the morally right decision. I know it sucks, deal with it. When its an inherited team, you might have to swallow it now just so you can change the team composition later. This is inevitable.
Be firm but fair. Other team members will be using this to judge how much they can trust you. Trust is the most important commodity and you don't want to lose all credibility by appearing biased. Juggling this and point #2 is often the hardest part of the entire process.
Try to fix it the first time around. Nothing is worse than dragging it out. If the issue isn't one that can be resolved swiftly and permanently, transfer one of the members to another team in a graceful way, making sure that everyone knows you aren't just dumping him. While these things MIGHT work themselves out in the long run, you shouldn't be betting the well being of you team on a possibility. This will send a clear signal to the members that you really do value the team concept.
There are other factors to consider as well but this topic is probably is little too wide to allow for clear and concise answers.
The best, most practical piece of advice I can give is to take the people out to lunch and talk to them about it. Don't bring up the issue directly, just ask them "How are things?" and "I've noticed you seem to be distant/pensive/frustrated/whatever" and let them speak. Don't judge, blame or take a position. Ask questions like "Do you think the team feels stress?" and see if they can articulate about the situation. Usually after about 30 minutes, you end up talking about the problem because they have raised it. (Of course, you planted the seeds to let them open up about it...)
Lunch is a great way to approach the subject in a low impact way, plus it lets you develop more of a personal relationship with the person (be sure not to talk only about work!)
Interpersonal conflicts happen all the time. I find many wash out in the normal process of teaming; as the team gels, so do its members. When it does not, there is no fancy process. Throw the offending parties in a room, timebox a discussion, and facilitate a resolution.
You are on a project, you have limited resources, and there are a ton of threats jeopardizing your success everyday. There really is no time to horse around with this type of garbage. And I think that message needs to come across to the offending parties, with the underlying message being that the grinding components will be replaced with new ones if this lubricant does not help.
Depending on the severity I and speaking very generally, my approach consists of two stages.
Stage one is to talk to each of the involved persons one-on-one to find out what happened and how emotional the problem is. The vast majority of the cases can be addressed and resolved with just one such conversation with each individual. In some cases I speak to one or more of the individuals several time. Depending on the situation I try to provide recommendations and advice. Having these conversations offsite, e.g. over a coffee at a nearby cafe, gives it a somewhat less formal tone. Choice or location and wording depends heavily on the situation.
Stage two is getting people into a single room and see how that works out. In my career I had only very, very few cases where this was required. Sometimes a meeting like this needs to be facilitated. In that case I think it is important for me as a manager to stay as neutral as possible.
Only in one case I then had to develop a plan to work with a person to continue their career in a different team. Last thing I heard was he was doing just fine in his new role.
Apart from the above I find - and that would be my advice - that in most cases interpersonal conflicts can be avoided or minimized by interaction with all team members so that all people have a sense of being respected, contributing to the team work and participating in the success. Communication is essential!
Of course there are a gazillion other factors that influence how I handle conflicts and my approach in specific cases can be substantially different.