In the recording studio, we primarily use large diaphragm condensor microphones for vocals. They have a beautiful characteristic sound that is sweet and sonorous. They hear the sound with a diaphragm, basically an electrically charged plate that sends a very small signal when it moves (by being pushed back and forth by sound waves).
These mics also have a very noticeable proximity effect. The closer you are, the more bass it has. I recommend finding your favorite sweet spot for your voice. There is not an absolute rule here on distance, but most people find somewhere in the 1-3 inches range is optimal for them.
Guitar players can benefit greatly by tuning the mic placement for their amp. Placing the mic directly dead center of the speaker at the dust cap gives the cleanest sound. It can be moved anywhere towards the rim to roll off unpleasant higher frequencies.
When singing and reaching for high notes, I do not recommend moving dramatically away from the microphone, if you can avoid it. Instead, ask your audio engineer about your compression settings. This audio effect can reduce the volume difference (dynamic range) between the high notes and the low notes, so much so that not much more than a nuanced movement should be needed. Pulling away actually makes the high notes rather shrill and unpleasant as a result of the proximity effect.
For live sound mics, like the Shure SM58 or Beta 58A, It's best not to cover the ball of the mic with your hand. It makes it sound muffled. Grasp the mic directly below the ball for best results.