Understand how your auxiliaries work. Your auxiliaries allow you to send the signal from a channel strip to somewhere else while maintaining the signal on the channel strip. For instance, you can use auxiliaries for monitor mixes for performers in a live environment. You can also use auxiliaries for external effects processors or a number of different situations.
Set the auxiliaries to pre-fader to allow you to change the level for the auxiliary with the auxiliary knob but not with the channel fader. Most mixers have a "Pre" button that allows you to enable pre-fader mode. If you don't have the button pressed, your auxiliaries are in post-fader mode, which means your channel fader will affect the signal level of the auxiliary output. For monitor mixes, you usually want to use pre-fader so you can control monitor mixes independently from the front of house mix. Some effects processors will be better to run post-fader, though, so don't always rely on pre-fader.
Send out your auxiliary sends. On the back of your board, you will find your auxiliary outputs. For a monitor mix, you will use these outputs to connect to the inputs of the monitors. When using an effects processor, you will use the auxiliary output to connect to the input of the effects processor.
Launch your auxiliary sends. On the back of your board you will find your auxiliary outputs. For a monitor mix, you will use these outputs to connect to the inputs of the monitors. When using an effects processor, you will use the auxiliary output to connect to the input of the effects processor.
Plug in a return if necessary. If you are just doing monitors, you do not need returns to the mixer. When using effects processors though, you need a way to get your effected signal back to your mixer. Take the output of the effects processor and connect that to the return input on the back of the mixer. Now you will have to adjust the return section on your channel strip to get the desired signal.
Use the auxiliary knob to set the desired level. Once you know if you are running pre- or post-fader, and you have your inputs and outputs all correct, you can start sending signal to your auxiliary output. Turn up the auxiliary knob until either your monitors are set correctly or until you have the desired amount of signal going to your effects processor or other outboard equipment.