This tut was modeled in 2.64 and 2.69. I am using 2.77. What version are you using. There are slight differences in the versions.
Couple things right off hand. He is extruding and scaling in the X,Y axis and then the Z axis. Also when he double bevels I would bevel only once with 3 segments and a profile of 0.5 . Yes he doesn’t explain every detail. If this gets you through this area let me know. If you need more I will give you detailed keystrokes. Again what version are you using? We can get through this. 😉