Most mixers have inputs for either XLR, 1/4 "jack and RCA connectors. Some mixers also have a USB or a FireWire input/output.
Condenser microphones require phantom power. This power runs trough XLR cables, and mostly has a voltage of 48 volts. The mixer has a switch to turn this power on and of.
This is the volume control of the preamplifier. With the gain button you can also lower the volume of the incoming sound.
Compression makes the volume changes smoother. On the right you see a picture to clarify.
This sets the volume of different frequency ranges. At this mixer are three buttons for the tone control; low, medium and high. More expensive mixers often have four buttons; low, medium-low, medium-high and high.
During studio recordings, it is common that the buds of the equalizer are all on neutral. When you have the original sound in the computer, you can make changes with the software you use. (Audacity or Cubase for example)
The red LED lights when the incoming signal is too high. It is advisable to lower the gain. If you do not have DI-box between the mixer and the source, it is wise to do so. If you continue without doing anything you might damage the mixer.
This sets the volumebalance between left and right.