I was totally confused too when it came to drift alignment tutorials, so I just experimented until I could see what was happening as I made adjustments to my mount. Explaining this successfully is beyond my ability, but I'll try.
Firstly, With the tripod level, I mount the Astrotrac on the tripod with the long section ("arm") facing in a Northerly direction & I level it so that the arm is horizontal. I then place a magnetic compass (pointing North) on the arm facing the drive motor (with the magnetic delination adjusted for my location) & rotate the mount "left or right" until the magnetic needle is centered on North.
Then, I tilt the mount (elevation) so that it is angled for my location ( I am at 52 degrees North, so I tilt it so that the arm is angled approximately 38 degrees). 52 + 38 = 90. I now know that mount is angled approximately 90 degrees towards the North celestial pole.
I then face the camera (on another tripod head that is attached to the Astrotrac) towards the South and angle it so that it's pointed above the horizon approx +20 degrees. I check that the stars are drifting left to right and level the camera so that the stars are crossing the viewfinder in a level manner. I then start the drive motor and begin a long exposure in "Bulb" mode on the camera (approx 5 minutes) and after approx a minute has elapsed, I block the lens for another minute with a piece of black card and then remove the card and allow the exposure to continue for three minutes.
I look at the resulting image to see how the stars have drifted. Note, the minute that the black card was blocking the lens will appear blank & this will indicate the beginning of the exposure. This exposure will also give me an idea of what settings to use on the camera when I decide to photograph the stars properly. The longer the trail, the more off target your mount is.
If the stars drifted left or right, your elevation is off. If they drifted up or down, your mount is off in an East or West direction. This is where the real confusion begins, so I'll try to give an explanation of why this is. It is important when doing drift alignment that you only concentrate on one direction at a time so as not to go totally wrong.
When you are facing North (in the Northern hemisphere) the stars rotate in an anti-clockwise direction & if you face South, they travel in a clockwise direction. The stars rise in an Easterly direction and set towards the West. Your camera is facing South and the stars in it's viewfinder are travelling clockwise. Your drive motor is also moving your camera in a clockwise motion to keep the camera moving in tandem with the star motion to counteract any drift.
If you can imagine two overlapping circles drawn on paper with directional arrows drawn on their edges. (one travelling clockwise = your mount and the other travelling anti-clockwise =North). Assuming that the circle representing your mount is overlapping the circle representing the North but is off to the right of it, the line drawn from your mount circle that appears within the North circle will be travelling up. Your mount is therefore off in a horizontal direction and needs to move left to get both circles overlapping with one directly over the other. Likewise, if the circle representing your mount was to the left of the North circle, the intersecting line from your mounts circle will be travelling down. This will give you an idea of how the stars will drift in your photos & what direction you will need to adjust your mount.
