Burn in procedure?

No,
You can burn interconnects even aside from the amp or components:

1. Connect the ends of an interconnect to the DMM test leads using an aligator clips
2. Connect one test lead to the HOT prong of the AC recepticle and another test lead to NEWTRAL prong of the AC recepticle

Here you go: you'll burn your interconnects insntantly!

For interconnects, and speaker cables, consider a "professional" accelerated burn in process lasting approximately three days, for about $20 to $30 at cableburner.com
I found that the gadget used by George Saubon produced a positive performance change, even on interconnects that were already well used, and already had been burned in specially by my using a special CD-R from Purist Audio Design.
For power cords, there is an inexpensive plug that allows you to "exercise" your power cord to the max. See archived past discussions about power cord burn-in for more detail on that topic.

Well, to burn in gear w/o buying aftermarket gadgets as listed above, with cables it is my understanding you need signal / current at least going through that cable, obviously. If you are burning in an interconnect on your CD player, you need to have the CD player running, obviously, but I do not believe you need the preamp on and I see no reason to need the amp on. I think you get the picture. For electronics, you need signal going through the piece you want burned in. EX. If a CD player, run the CD player; if a preamp, run a source to the preamp and have the preamp on; an amp would need all three on. Again, you get the picture. A side note, on an amp, does the volume level matter??? That I don't know.

Brian

Hi Paul
Basically you need a signal-source, a load, & the resulting signal-current flowing through the cable. So let's go through a typical signal-chain...
Let's say that you are breaking in the interconnects from your CDP to preamp & the CDP is running in repeat mode. The interconnect cables running to the preamp will only have signal-current flow if there's a load connected, which means that the CDP's input must be selected at the preamp input. If you have it set to (tuner, phono etc) then the signal-circuit is open & no current flows, thus you are not breaking in that cable. The preamp typically doesn't have to be powered up (unless you have a relay-driven input selector design such as Accuphase --- no power = no relay = no load) but that's an atypical situation.
If breaking in the interconnects from pre to PA then yes of course the pre must be on & passing an input signal through to its' outputs. The signal load is then the amp, & no it doesn't have to be powered on.
If breaking in the amp then yes of course it must be powered on & passing a signal output to speakers or to a resistive dummy load. Just leaving the amp powered on (but passing no signal) will not breakin anything.
Whatever you do, avoid the AC power scenario as posted above. The only time you get involved with that is when breaking in AC power cords. Member Subaruguru (Ernie) has a slick & inexpensive AC adapter harness available for such purposes. It's so cheap & easy to use that I didn't bother to build by own instead.