The first thing to keep in mind when dealing with conflict in the workplace is that some conflict is normal when human beings interact. Conflict actually contributes to an effective group dynamic in the sense of leading to changes that need to be made. That said, too much conflict and unresolved conflict can become a problem, in the workplace or elsewhere. Communication is the key to resolving conflict, both in keeping it to a healthy minimum and making sure that all parties understand appropriate limits and know that their perspective has been considered in the resolution process.
Establish conflict resolution policies for the workplace. These policies should be written (or at least reviewed) by a trained human resources professional. They must include at a minimum an emphasis on respectful communication between all interested parties and the specific steps to be taken in the conflict resolution process (and who to contact to begin the process).
Minimize areas of conflict among employees. Make job descriptions and individual responsibilities clear so that there is little ambiguity. Maintain a company culture focused on organizational goals rather than individual goals to minimize conflicts of interests. Give rewards and bonuses to teams and not just individuals.
Provide sufficient resources for all employee needs. Competition for work resources, whether it is the only computer with enough memory to run a new app or the copier that scans the fastest, is a common cause of employee conflict. These kinds of resentments and problems can be minimized by providing adequate resources so employees do not feel they have to compete for them.
Emphasize resolving workplace conflict as a "win-win" situation. If you step back and consider that the conflict began because one party (or both) felt that the other was interfering with his ability to do his job, then resolving the conflict results in a more productive workplace (and not resolving the conflict just maintains an unhappy and less productive workplace).
Address all conflicts as proactively as possible. While you want to give individuals a chance to resolve minor situations informally, you also want to minimize conflict at the workplace, so it is wise to nip conflict situations in the bud. That said, if the situation has escalated to a formal complaint, it is important to abide by the company conflict resolution policies so that everyone is treated fairly and the interests of the company are protected.
Consulting with an experienced human resources professional is a good idea before trying to put a comprehensive workplace conflict resolution plan in place because there can be legal and regulatory considerations for the business.