Driving up a very steep mountain road with a manual transmission

Don't use the brake when going up, it will only make it more difficult.  Just stay in first and below the red line RPM.  You don't really need to shift at all while going up and you don't need to go fast up the hill, but keep it fast enough that it will not stall. 

BTW on the way down, keep in in first gear to help slow the car down and not overheat the brakes. 

My daughter has a house with a drive like that. I really hate driving up that drive.