The key element in sound engineering is the proper use of microphones. There are many microphones used in live settings and in recording studios. The most common vocal microphone is the Shure SM58, which is a dynamic mic. Although not used in the studio as extensively, it is the industry standard for live performances. It is built tough and has a lovely sound as well as a wide frequency range to capture the subtle nuances of a vocalist.
You can use many microphones on drums to capture individual pieces, including condenser microphones that readily capture the high end more capably that any other type of mic. Use two to capture the room ambiance during drum tracking. If you set them near the cymbals, you can get a great sound. The sister microphone to the SM58, the SM57 is often used for the snare drum and tom toms. Use a mic that can handle bass frequencies such as the AKG D12 for the kick drum. This microphone can also be used for the bass cabinet.
Guitars are captured using an SM57 as well, but there are many models of microphones available. Many sound engineers use multiple brands of microphones on a single speaker to get a unique combination of sounds. You can place the microphones in different areas of the speaker as well as different distances to achieve a variety of sounds.
Another key element of sound engineering is the process of mixing, whether in the studio or in a live setting. The engineer must make sure that everything is placed correctly sonically when a band is performing live. The audience would like to hear the musicians as they would a CD or mp3, so the sound engineer's job is to use compressors to even out the sound and the equalization to make instruments sound pleasant in the particular setting. He also uses the levels on the sound board to highlight key performances and certain musicians such as vocalists and soloists.
In a studio, the sound engineer's job is to ensure that the instruments and musicians are recorded well and that the tones of the instruments are strong and represent the musicians well in recorded form. To do so, he uses techniques of equalization and microphone placement to achieve the desired sounds. By moving microphones and changing room dynamics, he can achieve just about any possible desired sound.