As an audio engineer, you must capture the best sounds possible from the performers and instruments. Using the latest techniques and the best equipment makes that be possible. It should be done with minimal intrusion to the performers.
Use a tube microphone to capture vocals. A tube microphone can add depth and warmth to a vocal performance in a studio setting. Although very expensive, most studios should have a tube microphone for you to use as an engineer.
There are specific microphones that should be used when mic'ing a drum kit. Use condenser microphones for your room microphones since they will pick up more high-end frequencies than a standard microphone.
When running live sound, mute any microphones onstage that are not in use; this will cut down on feedback. Also, use drum shields when possible to isolate the drum microphones from any possible interference from stage monitors, including the guitar and bass amps that are onstage.
When recording or mic'ing guitar amps, try to use one microphone on-axis, facing the center of the speaker cone, and one microphone at a 45 degree angle off-axis, pointed toward the head of the other microphone. This will provide a more full sound and add depth and character to the guitar tone. This can also be done in a live band setting, just be wary of any phase cancellation you hear and make adjustments.
In a live music engineering setting, use the volume faders on the vocals to accentuate vocal phrases to add excitement to the performance. Also, heavy delay at the end of phrases may add depth and character to the vocal performance. There are many subtle ways for an audio engineer to make the artist or band sound extraordinary.