Approach the meeting by keeping in mind that the discussion may lead to an amicable solution.
If the employee makes suggestions, you can suggest amendments or alternatives to try and encourage a solution.
If you need to, explain policies and management decisions to the employee to help them understand different points of view. This may result in you finding common ground.
Remain calm and objective at all times even if the issues seem to be personal.
If new issues are raised, then adjourn the hearing so that you can investigate them.