Few shots will put your mechanics to the test like shooting when the cue ball is frozen to the rail. For starters, you don’t face shots with the cue ball on the rail too often, so there is an inherent lack of confidence in your ability to stroke the shot smoothly.
Also, because these shots don’t come up that often, shot from the rail are rarely practiced with any frequency. Not sure why that is the case. They should be.
There are several factors which make these shots problematic. First, you have to take into account that the rail is higher than the middle of the cue ball. Cueing center ball or below is not possible. Also, the rail itself makes it virtually impossible to keep your cue completely level. You will always be striking the cue ball at a downward angle. Particularly with amateur players, you will see a lot of miscues shooting a cue ball off the rail because the player tends to bring the cue back at one angle and stroke forward at an upward angle. And, under no circumstances should you attempt to use English on these shots! You must keep your contact along the vertical axis.



Suffice to say, getting a solid hit on a cue ball that is frozen to the rail is difficult.
So, how do you get comfortable with shots off the rail? For starters, give this shot ample time in your practice regimen. Gaining a level of comfort and trust is really important, and that comes with repetition.
As for actual drills, try the shot in the diagram. Place the cue ball on the long rail, one diamond from the corner pocket. Place an object ball in line with the opposite corner pocket, about a foot away. Simply work on pocketing the object ball as if it is the last ball on the table. Don’t concern yourself with playing shape for a follow-up shot. Shoot this until you can’t miss.
Once you’re comfortable with that shot, make the shot more difficult by placing the object ball at a bit of an angle from the corner pocket. After practicing that shot, add distance between the cue ball and object ball. Move the shot around the table a bit, shooting to the side pockets. Progressing through this drill will do wonders for your confidence and success rate with shots off the rail.