This is how I check my spokes:
You have a total of 64 spokes on the bike, 32 on the front wheel and 32 on the back. You have 16 spokes on each side of each wheel, and of those 16 spokes, 8 face "clockwise" we'll say, and 8 face "counterclockwise."
I start on one side of a wheel, check clockwise spoke #1, mark it with a piece of chalk, then rotate the wheel 180 degrees and check the opposite clockwise spoke, #5, then rotate back to #2, then to #6, #3, #7, #4, and #8. It doesn't matter which spoke you designate as #1 as long as you keep track of where you are in the order based on where you started. Now, staying on the same side of the wheel, I do the same thing on the counterclockwise spokes. Having completed 16 spoke checks on one side of the wheel, I repeat the process on the other side of the wheel.
I noticed above that gunslinger and oldrider above is doing essentially the same process, except it is more of a "star" pattern. That works just as well or better. They are keeping track of which spokes they have checked while alternating which side of the wheel they are working on.
When I "check" a spoke, this is what I am doing. I use an extended 5mm hex bit and a torque wrench that will work at 53 inch/pounds. I loosen the spoke about half a turn, then tighten back to 53 in/lbs. I never have more than one spoke loose at any given time. I have tapped spokes with a wrench to hear their "tune" before, but I prefer a more objective means of evaluating their tightness.
You should also look for wheel damage, bent spokes, corrosion, etc. Maybe put zip ties on each intersection of spokes.
Once you've done it a coupe of times you can check all 64 spokes in 30 minutes easily.