How do you learn to pilot a private submarine?

If you purchase a sub from a reputable company, like US Submarine (an example, not an endorsment) the price will probably include training. If you choose to build your own then read, read, read and practice, practice, practice. Start in shallow water. Watch a lot of movies; both fiction and documentary and lay yourself out an intensive program to handle any contingencies you can think of. Learning to Scuba dive would be a major bonus in case worst-case scenario.