I picked up a non functioning Peavey Classic 20 combo amp off of craigslist today. The red jewel light lights up when the power switch is turned on, but no sound at all. The tubes ( 2 EL84's and 2 12AX7's) do not light up or get warm with the power on. I replaced the tubes and still no sound and no glow from the new tubes.

The treble pot does not move very smoothly, A visual inspection of the components of the circuit board show no obvious damage.

I bought this amp in part to learn how to troubleshoot tube amps. I guess the next step would be to go through the components of the circuit board with a multi meter and try to find a bad component. Any ideas on how to find out what's wrong with this amp?
I would suggest to replace the pot first. Likely the internals are busted which could cause shorted contacts. If that is not working properly it could throw the rest of your diagnosis. Then I would check the heater fuse for continuity. That should be F2. Check F1 (which should be right beside F2) as well, which looks to be both the mains and the B+ fuse, just to be sure it is properly rated. Since the amp powers on (pilot light) I would think the fuse is working. Checking the rectifier diodes would be smart as well.

If none of that works, good luck. The tubes will not emit electrons (making sound) unless the internals are hot. So presuming F2 is fine, properly rated, etc., you have to trace the PCB trace all the way from the power transformer leads, past the fuse, to the tube filament pins themselves and find where either a bad component is, or where the PCB trace is destroyed (and then jumper wires). Hopefully the power transformer itself is fine, but checking the taps to be sure they are putting out proper levels is smart.

Unless you need the amp on (which for most of this you do not), you need to know how to drain the filter caps. They can contain lethal voltages even with the amp off and unplugged. This video describes a typical process for draining caps. Do not assume they are drained, though, always check the amp after draining.

A Youtube channel I have learned a lot from is Uncle Doug.
Thanks for the reply. I watched that video, and others like it to learn to drain the filter caps. I'll try and post some pictures when I track down the problem and find the solution.