بسم الله الرحمن الرحيم
There is no addition or changes in the arkan (acts) of Hajj-e-Badal and its method. What you have to do is just say while making the intention that you are doing Hajj-e-Badal from so and so person. After that you should perform all other rituals as you do in normal Hajj.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.