If microphone selection and placement, monitor placement and volume control, and training your “talent” to project their voices don’t defeat any feedback issues you are having, then the next step is to work on “ringing out” the offending microphone.
This is the process of identifying what frequencies are feeding back through that mic, and surgically cutting those frequencies through the use of a parametric EQ.
Modern digital audio consoles make this process easier as many will show you via a frequency display where the feedback is occurring. However, older analog consoles will not have this, and lower-end digital consoles may also lack this capability.
The first thing that’s needed is an equalizer section of your audio console that has at least one fully-parametric EQ band. (The more that are fully parametric, the better.) This means that the band has control over frequency, gain, and Q (or width of the band). Some EQ bands will not have control over the Q setting, which makes them mostly unusable for dealing with difficult feedback situations.
If you don’t have a real-time frequency display on your audio console, here’s how I identify the frequency where the feedback is occurring. I pick the band of EQ that I think the feedback frequency best falls within (this comes through experience), set the Q to as high a setting as possible (A high Q number means a very narrow band of control), set the fader to be just below the point of feedback, set the gain of the EQ to increase the band I’m controlling by 6-10 dB, and then slowly start sweeping the frequency knob until the feedback begins and is at its strongest. (Be careful not to damage your loudspeakers!) Once the frequency is dialed in, change the gain knob of that band to now reduce that frequency until you get the volume you need from that microphone without the feedback. If your console has a real-time frequency display, you can visually see where the feedback is, making it simple to dial in your EQ band.
Sometimes once the primary offending band is cut, another band starts feeding back before you get the volume you need. In that case, you need to repeat the process with another fully-parametric band of EQ on that channel.
If you’re dealing with a very challenging mic and you run out of fully-parametric bands of EQ, you either need to add in an external EQ with more control as an insert into that channel (for analog consoles), or for digital consoles, there may be a more sophisticated EQ plug-in effect that you can add as a channel insert. When ringing out choir mics at the church I serve at, we had a lot of frequencies that were causing us issues. I found a parametric EQ plug-in that I could use as a channel insert on our Yamaha QL5 console that provides three notch filters (a band of EQ with a super-tight Q), and eight fully-parametric bands of EQ. This helped significantly in ringing out our choir mics.
Note that the more bands of EQ you use to ring out your choir mics, the more you are changing the tonal qualities of that channel—sometimes to the point where, while you are now getting the volume you need, it actually sounds terrible. Ringing out mics should be your LAST option for dealing with feedback. Your best plan of attack starts with lower on-stage monitor levels and teaching your vocalists and pastors to project their voices in all circumstances.