Amp hum attenuation...

Well,  being a simple guy...  I think we have to find it before we can reduce it.  I have many amps, many effects, yards and yards of cable,  many guitar types,  many other system components such as pre-amps, phantom power suppliers and the like. Sometimes you have to start at the beginning - and this is an over simplified process.  You may have to dig deeper into a step.   
 
Step one.  Unplug everything in the room.  This will be a isolation starting point and help to protect your gear for step two.
 
Step two.  Go to the circuit breaker and find the breaker for the room.  Turn it off.   Check to see it affects only that room.  If things go off in other rooms, unplug the stuff in those rooms.  Turn it back on.  We need to find out if that circuit has other items on it.  While this doesn't isolate us completely, its a starting point. 
 
Step three.  Beg, borrow or buy a inexpensive circuit tester - one that has the ability to check for open ground, open neutral, open hot, hot ground reversed, hot neutral reversed.   Test the circuit.  If it fails,  then have it repaired by a qualified, trained and insured professional. I do it myself - but I'm a nut case. 
 
Step four.  Plug in one amp.  Set the gain to your liking.  Find a known working guitar cable, plug the guitar in.  Note the noise.   Note your seating position and use this position for all other tests. EMI\RFI patterns can build up all over the room depending on the density and type of the electronic 'toys'.   If you fail with the amp alone and a good working grounded circuit, it could be the amp or the entire energy source.  I've had both happen, more than a few  times.  If its the energy source, it could happen intermittently or time of day.  I hate when that happens - somethings putting noise on the line ahead of your house and that tends to be the hardest to fix because its out of your control - call the power company.  Guys who perform for a living know all too well the variability of power quality - they try to afford power conditioners and voltage regulators for a reason. 
 
Step five - plug in your guitars one at a time and listen so that you have a reference for each type and quality of pickup you have.  This noise will be enhanced greatly by the pedal board step below.  Try plugging in each instrument cable you use.  Listen closely - these little hoober doobers are great EMI\RFI antennas.
 
Step six.  Plug in your PC, monitor, 'sound card', playback amp, speaker and microphone with good known working cable.  Turn them on.  Sit in the 'test' position with your guitar and amp running - you will use this position for the entire process - by staying in one position, you are testing for the combination of EMI\RFI buildup. Note - PC's and some monitors emit a healthy dose of noise.  One of the posts points that out - you can be sitting three feet away with pickups pointed towards the PC - monitor.  Turn away by 180 degrees and the noise drops noticeably.   Record.  Everything OK still?
 
Step seven. Testing pedal board components - power supply, cables, wall warts, effects units.  A healthy dose of both EMI\RFI injection (adding noise) and reception happens in this area.  In my personal experience, a large portion of 'NOISE' or buzz comes in here and it can take hours to shake out.  
 
As a point of reference, I run a Voodoo system - everything is racked, and my cable runs are inches, my cable is the best quality I can afford, I have each cable made by a really good sound company out where I live - they test for capacitance and noise rejection (anal, I know),  I listen to each effect as I am adding new ones to 'know' the buildup of noise they add, I use a power conditioner\ voltage regulator that the entire system is plugged into, I also use a quality power supply for the pedal effects.  I am noting this to show you can go to expensive and great lengths in the chase for eliminating noise.  By the way, wall wart devices that are digital tend to have a propensity to add noise - and a cheap power supply can transmit noise between devices. 
 
Plug in one effect - cable it up, plug it in to its power supply and listen.  You are now adding both noise injection and reception - you will get a buildup, and note it. add the next effect and so on, stopping to note the noise.  If this step passes - SUPER!!  Most of my failures come here or the next step.
 
Step eight - add another amp(s) one at a time.  Don't cable it in, just turn it on.  Sometimes amps have issues where just running a second one on the same power leg can cause hums and buzzes, even when they are not connected together via the effects pedal.  OK?   Then cable it into the pedals.  Note - you may be running effects in the effects loops of each amp.  Those effects could be plugged into the same power supply and a noise from one amp is injected into the other amp just from power supply association - happened to me with a set of eventides, and those are designed and built by a QUALITY company. They didn't add the noise, the one amp interacted with another amp through the devices, via the power source.  An easy way to get a bit of noise is to connect both amps effects loops into the same effects device (stereo).  
 
Step nine - my guess by now you've found that you have a sum of things causing the buzz or noise.  To finish it off, start turning on the 'other' things on one at a time, in that room and any room associated to the same circuit...
 
You should have been able to isolate the exact point, or become familiar with the summing of noise that you are hearing through the entire chain.  Theres a lot more you can do - it usually just comes down to a simple test of isolation, then adding, then listening to the sum of the components at each point..
 
Take care..