Attach the power cable to the mixer board and plug it in. To make any audio that you run into the board audible, you'll also have to run cables from speaker outputs on the board out to audio speakers. If it is not a powered mixer, you'll run cables into a power amplifier first, and then connect speakers to the amp.
Assign your inputs. Each source of audio that you want to control needs to be assigned to a specific channel on the mixing board. Each of these channels will have their own controls for level (volume) and equalization (EQ) as well as a pan control and a mute button. There will also be auxiliary sends for sending these signals to outboard effects processors, such as reverbs, delays, compressors and returns, for the return of the treated signal.
Adjust the level of signals going into your mixer by means of the gain control. Sometimes labeled "trim," this is usually a knob at the top of each individual channel strip. Once this level is set, you'll use the fader on each channel to control the volume of each signal. The master fader will then control the overall level of all of the audio signals in the board.
Take advantage of sub-groups on the mixer. You can route several signals to a sub-group and have the volume of all of them controlled by one fader. As an example, you could make a sub-mix of all of the drum channels and then assign them to one fader so that you can control the level of the entire kit without having to change the levels of each individual channel.
Watch the levels. The meters will show the audio levels of the signals going through the mixer, and are marked with negative numbers all the way up to zero, at which point the positive numbers go into the red. Make sure that the meters stay out of the red, and keep them at or below zero. Doing this will help keep the audio nice and clear--failure to do so will likely result in distortion that will quickly undo any fine-tuning you've done on your mix.