How does my incarcerated husband get divorce process started files and complete?

He would have to have a lawyer file the motion with the Clerk of the Court. It would be difficult (but not impossible if he is sharp) to write a motion and mail it to family court. If he does this, you as the opposing party will be notified by mail of the motion and the allotted time to respond. The whole process could take months to accomplish. The judge might be reticent to rule on it until your husband can appear before them to answer questions, etc.