There's one trick about motion for drawing straight vertical lines which makes it easier:
- the drawing tool should be leaned on your ring finger and rests on the recces between your thumb and index finger while supported by middle finger and blocked with the thumb; the pinky is supporting the ring finger and index finger is not used at all. The palm top is slightly rotated to the down, so your hand is more "horizontal" (or rather top of the palm is a bit tilted tilted to the surface you draw on).
And there are a bit different mechanics for short and long straight lines:
- for short ones (not more than few centimeters) you use only the finger simultaneous movement, a bending moment into the palm. no wrist, no elbow no shoulder. Quick moves, hand a little suspended in the air or based on a surface (better for beginnings)
- for long lines: you have absolutely stiff wrist and fingers, the main movement is in your elbow and shoulder and must be paralel - if you are a person who keeps the arm close to the body it will be mostly the shoulder, if you are a "sweepy" drawer it will be mostly the elbow. In both cases avoid slow moves, but you'll see they are much slower than in the short line method.
Keeping the whole arm stiff will help in drawing clean lines. You should not rotate the paper or your torso to make it easier - it's a bad sloppy habit that would not help you in the future and the one that should be blamed for the misshapen and lopsided lines after you get used to it.
For the long lines: Keep practicing a simple exercise - for few minutes draw straight lines again and again in one direction, first the vertical or horizontal ones, then switch the angle and/or direction, and so on - a whole bunch of different angles with lots of lines; change angle/direction after you feel comfortable and steady for a moment or two with one. You should use the whole sheet of paper (the best would be sth like ISO A2 format). Repeat this exercice multiple times and you'll feel the difference. It's actually a very basic and popular exercise for beginners in the drawing courses for architecture exams (at least where I live). It's not only for vertical lines, but for straight lines and directional drawing in general, but improves the vertical lines the most.