My arguement though would be that if after doing that 5 or 6 times wouldnt you realize you are doing something wrong? At the level someone in that boat is at I think a technical explanation of aim point and contact point or throwing all the aiming methods out there are them will just confuse them. This is why practicing is the best thing that is going to solve this problem in my opinion. Since I am still *new* I can remember how I learned things which is why I sometimes think those of you who are *more experienced* have somewhat lost touch of because it was so long ago and now you may overanalyze it.
From a newer play to you.... this is what i would suggest. Practice practice practice... take the cue ball line it up with the object ball so its straight in on the pocket and touching the object ball *frozen*. That is the part of the cue that has to make contact with the object ball to put it in the pocket. You can move around the table and look from different angles... that is the CONTACT point. That is where you need to hit the object ball to pocket it as long as you are hitting the center of the cue ball (not applying english that will alter the path of the object ball) and do not hit it really hard as that may also alter the path of the object ball to the pocket... (I believe that is called throw but im probably wrong on that as well)
As far as how I practiced all of this. Start with the object ball fairly close to the pocket so you have a little more more margin for error. Start practicing cut shots that are just off from straight in. Then start moving to a greater cut angle. As soon as you are able to make those shots, move the object ball further from the pocket and try again. (make sure you are hitting the center of the cue ball with a smooth stroke)
Once you are able to now understand where you need to hit the object ball to cut it in... put it agains a rail maybe 5 inches from a pocket. Try to cut that in from different angles, then move it further from the pocket and repeat. Being on the rail will give you a lot less margin for error, you need to split the hit 50% object ball and 50% rail (for now) later you will be able to hiit the rail first with a little bit of english and pocket the ball but for now cut it 50/50.
After you have successfully been able to pocket the object ball on the rail... put the object ball back in the open and place another ball near it but not directly in the path, this will teach you to concentrate on the ball you are trying to cut it and not the other ball in your line of sight. You can either put the ball next to where you will be making contact with the object ball or someplace down the line near the pocket but make sure its not in the way, its merely there to get in your head. Once you can do this put a couple other balls out there to try to distract you... as long as they arent in the way you shouldnt hit them if you just worry about hitting the object ball where you need to.
Then comes english but you then have to adjust for it and that is something you dont need to worry about yet. To clearify though... the reason I say center ball hit on the cue ball is because if you put draw or follow or left and right english it can potentially ad variables into the situation that you arent going to be able to consistantly learn from at this point. Figure those out after you get the basics down.
I practice cut shots every day that I shoot. Whether its from one end of the table to the other putting all 15 balls into the corner pockets a few times from different angles, to cutting all 15 balls into the side pockets from both ends of the table. (I am usually afraid of side pockets so I do this drill to get my confidence up when im playing on a new table it also lets you see how the pockets are) Develop your own way of doing drills and so on based on what you need to learn and practice. Once you get the basics then you can throw some more wrenches in there.
Images:
Shorter Cuts to start with:
Then move on to longer cuts:
Rail cuts require a 50/50 split hit for now:
Then start to learn to ignore the other balls on the table:
If you think you would rather learn aiming systems... then check out some of the following posts...
a Search for "Aiming Systems" Personally I think practice and finding what works for you is a better option.
Good luck
Keep in mind this is just MY suggestion and how I would do it but everyone will have their own way.
-Lou