How should I do the procedure to visit Vladivostock from Hei Long Jiang Shui Fen?

I think you may mean you want to go to Vladivostock from Suifenhe City, right?
If so, I heard there is direct train from Suifenhe to reach Vladivostock and the train is K7023.
For other matters, I think you may need to get a permission to enter that city first and then to pass through other procedures.