Love Him Out The Door. I do not mean just be nice to him, but do everything you can to provide a smooth transition. Be overly kind, generous, and helpful. Go way above the call of duty toward him and his family. If there was a moral issue, provide him a huge amount of counseling. Not two sessions, but spend 2000 dollars if need be. If it is a lack of performance, give him a heads up that you are going to make a change, or outline the concrete steps that must happen for him to stay. Usually, if it got to this point, it is going to end in a firing, so give him time to find another opportunity, and give him a defined end date too that is 6 months into the future. If you feel that he will not handle this well, give him 6 months of salary, allow him to stay in the house, and bite the bullet, and refuse to be cheap. It will pay for itself in the long run.
Sometimes a church will give the preacher one week of salary with the news of being fired. Each time I have seen this, it has created a church fight. There will be people who will advocate that the preacher be fired, and given nothing. Never, ever, listen to them. At the end of the day, people are going to complain no matter what you do. You are too harsh, you are too generous. But trust me, people can follow an eldership that was too kind, too loving, too generous than one that was too harsh. If you are going to make a mistake in stewardship of the Lord's resourses, be too generous.
Never Forget About The Family. You are not firing a preacher, you are firing a family (unless he is single, but I bet his Mom will still be mad). Always remember his children, and his wife. The children will struggle with what is happening. These children will need to move and make new friends. It will be hard for the kids. The wife will feel the pain of the firing often even deeper than the husband. In the firing process, there needs to be a transition plan for the family. If the minister is reasonable, bring him in to create a transition plan with the family in mind. Hire a ministry coach to help the minister through the process. If you are going to fire him, take the time to look for resources and coaching to help him through the transition. If you have not done this, you are not ready to fire him yet. Slow down, and think.
When the Preacher Acts Like a Fool. Underneath the problem with these cases is the lack of trust between the church leaders and the minister. Trust has dissolved between the parties. This means the elders are seeking to protect themselves and a minister is seeking to protect himself. And sometimes the preacher acts like a fool and creates division. There are a couple of things to do. Create an incentive for him to act his best. Call it a bonus, a positive recommendation, or help. Trust is not there, but people can see self interest. If he cannot handle himself well, lead the communication within the congregation, and do not allow him a platform. Elders must protect the flock too from division. Do everything you can to avoid a church fight. When two bulls fight, it is the grass the suffers.
These are always hard times, but forethought can lead to better transitions. Slow down, and think through each step.