First of all you should realise that it happens at almost every workplace so do not panic in case of any conflict between employees.
You must know the reason of this conflict otherwise you will not be able to resolve the issue wisely. You may face trouble in finding the truth as both parties will have their own version but take help from witnesses to determine the facts.
Listen to them attentively. Call them in private and ask them what went wrong. You can have a joint meeting but do not let them argue in this sitting. Try to evaluate their mental condition before and after the conflict as it will really help you find the reason that inflamed the situation.
Ask both parties to come up with suggestions to resolve the issue. Let them suggest each other a series of positive steps and reach a consensus. If the problem is a bit complicated than you can take help from Employee Assistance Plan (EAP).
Encourage them to sacrifice for each other as it is the only way to bring harmony at the workplace. Tell them that everyone has to compromise to find common ground and they should learn to forgive each other.
The negative things that happened during the conflict should be worked out otherwise it will not be a permanent solution and you will face such conflicts again in the future.
You should be positive and optimistic. Encourage them to see things in a larger perspective. Try to transform this negative conflict into a positive competition that will elevate their performance.
You should support the right thing tactfully but do not take sides.