How to start the process of getting placed close to my spouse(e1 sailor recruit) Navy?

Your branch manager and their assignment detailer talk to one another. You probably won't be able to move until you're eligible to reenlist to move. But they can let you know where your spouse will be stationed

For future information; Navy terminology It will be Seamen, Airmen, or Firemen recruit E1, apprentice E2, not sailor. Until they are an E-4 at that point they are generally identified by Rate and class but all small and insignificant.

Your first step in to enroll in the Married Army Couples Program, although, you won't be able to enroll until she is on active duty. She will need to enroll in the Navy's equivalent program. It is possible that if you both get the enrollment done as soon as she comes on active duty, her detailer maybe able to assign her to the same geographical area as you. Your chances are better if she has an MOS that can be utilized every where or you are stationed near one of the coasts.