The simple secret: Relax your fretting hand before you move to the next position. This is a subtle move, but can make a huge difference in the clarity and efficiency of your playing.
There are two advantages to relaxing your fretting hand before/as you move: 1) it MUTES the strings as your fingers leave the strings; and 2) it avoids sounding the strings due to “pull-offs.” In other words, by relaxing your fretting-hand fingers as you release a chord you avoid sounding a potentially wrong note as you move to the next position.
The Exercise: Get a feel for this “relax first” move by squeezing and relaxing a chord WITHOUT leaving the strings. Using a simple C chord, for instance, squeeze it, then relax. Do this over and over: squeeze/relax/squeeze/relax. Maintain contact with the strings!
When your fretting hand is relaxed, move SLOWLY and directly to a different chord – D major, for instance. If you do this correctly, the open strings should make little or no noise as you leave the first chord and land on the second.
As you move, keep your fingertips close to the strings so that the distance moved is minimal. You remember the old axiom: “The shortest distance between two points is a straight line.” Be efficient and direct. It will help with both speed and accuracy.
We will deal with lateral-movement squeaking (sliding up and down the neck) in another installment.