Connect an XLR cable to a microphone. Connect the other end of the XLR cable to the "Input" jack on an audio interface. The audio interface converts the audio signal into a data stream that your digital audio workstation, or "DAW" can interpret.
An audio interface is necessary to convert the audio so the computer receives it as data. The connection method varies according to which interface you have, but it typically calls for either a single USB cable or single Firewire cable. Connect the relevant cable to the relevant port on the rear of the interface and to the correct port on the side or front of your computer.
Open your preferred DAW, for example Cubase or Digital Performer. Click "File" and select "New Audio." Although the output signal will be a stored sample, the input signal used to trigger it is audio from the microphone, so Audio is the correct channel type for this application, rather than MIDI.
Plugins are third-party software applications that you use as part of the proprietary control suite that comes with your DAW. There are a variety of trigger plugins, such as the Koen KT Drum Trigger, and depending which program you use, there may be one included with the install. For example, the Digital Performer features the "MOTO" trigger plugin. Assigning a trigger plugin to the audio track enables you to specify the output sound as something different to the input sound.
Because the plug in is triggered by audio, it's necessary to set a sensitivity parameter, otherwise any sound, including background noise, could set off the trigger. Typically the audio for a drum trigger is a drum, which is loud anyway. Adjust the "Threshold" dial high.
Now that the input signal chain is configured, the output sound must be assigned. It's necesary to set a MIDI channel as the output, in order to assign a prestored audio sound. Click "Send To" on the audio track to which you assigned the trigger. Select the MIDI channel with the assigned drum sound. This configures the audio channel to send a trigger message to the MIDI channel, which outputs the selected drum sound, rendering the microphone as a fully-functioning drum trigger.