Not intending to insult your intelligence, but titling your thread “Connections” sounds like you just need help hooking everything up. If this is not what you’re looking for, then please clarify in a subsequent post.
So - you didn’t give any details on your sound card (like make and model), but it has to have phantom power with a mic pre-amp and XLR input for the measurement mic. Presonus AudioBox iTwo is an example.
Given that, the sound card plugs into your computer via USB. The measurement mic plugs into the sound card, with phantom power enabled. The audio output from the sound card plugs into a vacant channel on the PA system mixer.
Regards,
Wayne