For the most part if you are right handed you aim with your left eye and if you are left handed you aim with your right eye. Right handed people miss more cuts to the right than they do cuts to the left. This is because they tend to have their head turned more to the left causing their right eye to see more of the shot leaving the left eye out of the sight picture. This tends to cause the head to try to move to the right during the stroke. This movement changes your stroke and can cause you to miss. But, on a left cut the left eye is more into the sight picture and the right eye is more to the right side of the cue stick. If you approach a right cut shot looking at the contact point of the object ball with your right eye because it is on your right side, you will favor your right eye.

Side Stick Aiming takes advantage of this by forcing your eye and head alignment as you go from a standing position to a shooting position.

Here is how it works.

Most of your aiming is done from the standing position, it is an integral part of seeing the shot. You point your cue stick through the vertical center of the cue ball in the direction of the object ball. If you apply English, left or right spin, you should do it after you have done your aiming.

If your target is a pocket, with your eye draw a line from the pocket through the object ball. Where the target line comes out of the object ball is the contact point. This is the point that you must hit with the cue ball.
Now from the standing position, place your cue tip at the horizontal/vertical center of the cue ball pointing in the direction of the contact point on the object ball. Let's say you are shooting a right cut shot. Move the cue stick while keeping the tip located at center of the cue ball until you align the right side of the cue stick to the contact point on the object ball. Place you feet into shooting position, put your bridge hand on top of the cue stick and slide it down on to the table as you take your shooting stance.
When you do this you will be looking down the right side of the cue stick to the contact point with your right eye. This will place your left eye more into the shot picture.

Each of your two eyes see a different shot picture which your brain puts together to make what you think you see. If you leave one eye out of the shot picture, that eye will struggle to get back into play and can cause you to move in a way that may make you miss the shot. When you force your right eye to move to the right side of the cue stick on a right cut shot, your left eye is moved into position to share the shot picture and stabilize your shot.

When you shoot a left cut shot you should look down the left side of the cue stick to the contact point on the object ball using your left eye as you move from standing to shooting position. This will move your left eye more to the right.

Most of good players do this with out even thinking about it and with practice you will also.

In watching many of the Philippine players, some of the best in the world, I have noticed that many of them start their shooting procedure by placing the cue tip on the table near the cue ball. I wondered why and after doing it for a while I found that this anchors my shot line and does not let me move off line while placing my bridge hand. Most players just drop into position but I find it is better to place my cue tip on the table while standing. Then I line up my shot from the vertical center of the cue ball sighting down the side of the cue stick. Then I place my bridge hand, palm down at the joint of the cue, and slide my bridge hand down into shooting position. From this position I can see the shot better and with both eyes balanced. It should feel like you can not miss.

See the following two diagrams that illustrates the right cut and left cut alignment.

I urge you to try this method and see if it works for you. I hope you will enjoy making more balls.