As a Pro Se in family law in King county superior court, what will be the process for deposition and getting subpoenas issued?

No, you won't. The clerks are legally prohibited from giving advice. Take a look on the court website, and you will see all of the basic family law forms there. http://www.courts.wa.gov, and the search engine will help you. It is fairly useful. Good luck. If you cannot afford legal counsel, have you already tried 211? This is the "clear' intake line, and if your situation involves certain issues, they can help you find representation if you are low income.

One of the most difficult things to accomplish as a pro se is "discovery" which is the process by which you gather information via depositions, interrogatories, requests for documents, sending subpoenas, etc. You may well want to have an attorney for this part of the process so that you are assured that you have requested the right information and followed the right process to obtain the information/discovery.