your request for information is generic in terms of what process, the # of layers, etc.
Using a 309/309L as a butter pass is quite common before going to the 316L overlay. The process mostly used is dependent on accessibility to the surface you will be welding. If the area is easily accessible, sub-arc welding is a common welding process for overlaying. If accessibility is limited, flux core welding is another option. Next, the number of layers will depend on the factored corrosion equation you are trying to maintain. Depending on your customer requirement you may need at least 1/4" of exposed 316L. Of course, it could be more or it could be less. Number of layers can also depend on whether the overlay will be machined down after welding, or left in the as-welded condition. Type of electrodes will depend on what process you choose. Finally, the required tests will depend on your customer specifications. I know this answer is probably not much help to you, but most of what you are asking is dependent totally up to you and the specification requirements.