This article explains in detail how to go about it, with attention to each individual instrument, and then blending the sound as a whole. To boil it down to the essential elements, there needs to be two separate mixes happening: one for the audience in the hall (i.e., “mains”), and the other on stage for the musicians (i.e., “monitors”). It’s a good idea to work on both mixes at the same time, trying to make the sound on stage and in the hall as natural-sounding as possible.
For example, get the drums and bass first, guitars and keyboards second, and then add horns, woodwinds, strings, and vocalists. Having a good blend for the instruments first will make it easier when adding in vocals over the top. Not adding a lot of reverbs or effects will make it easier to hear all the instruments. They can be added after creating a good mix “dry” (without effects). There’s definitely an art and some science involved with live music Sound Checking.