Vintage tube amp resurrection with Variac?

I have acquired some vintage tube equipment that has not been turned on for several decades. I bought a Variac on eBay having read many times to be sure to "bring up" old tube gear "slowly on a Variac". What exactly constitutes "bring up slowly"? Is it some sort of staging perhaps? If so, what voltage at each stage, number of stages, how long per stage. Or does it mean to continuously, but very slowly, crank the Variac from 0 to 117 volts?
I have used a variac to bring back equipment that hasn't been turned on for a year or two, but decades is another story! My method is to start out at zero and bring up in either six or twelve volt increments (I use these values because they divide into 120 VAC by factors of ten and five respectively) depending on how long since the unit was last energized. Twelve volts if it has been a year, six volts if it has been more than a year. I also vary the length of time at each increment depending on how long since last energized, 10-15 minutes for a year or less and 15-30 minutes for more than a year. I would suggest you move up in 6 volt increments and leave it at each increment for at least 30 minutes. The whole point of this is to reform the capacitors, after decades they may very well be bad, but it's worth a try. One other comment, my variac has a tendancy to blow the circuit breaker when first plugged in if the load is attached, not sure why, but I start out with no load, make sure it is at zero volts, then plug in the load.
That paranthetical bit should be factors of twenty and ten, not ten and five. Hit the Submit button when I should have hit the Preview button!
Don't forget earplugs and safety goggles.

I have done this a few times using this technique. There are different opinions out there, but an excellent audio technician told me this is what he did, and never had a problem, so that was good enough enough for me. Make sure you have speakers or load resistors on the outputs. Not having a load on the outputs could cause a serious problem. Also, watch the tubes as you increase the variac. If there is a major bias issue, the plates of an output tube may start to glow red. If this happens, definitely stop the process, as it will be best for a technician to take over.
@OP, I'm not a tech and that's what makes my post worthwhile.

Knowing what I DO know is enough to say that rather than screw around with your old amp, I'd have it looked over by a reputable tech. If the manufacturer is still around... even better. I bet the old PS and coupling caps are dried out and need replacing. Other parts may need to be replaced too. Here's a quote from TLS49's article:

"You should probably consider replacing the capacitors on an old piece of equipment even if it doesn’t hum. Old filter caps will fail sooner or later, so you may save yourself some time and trouble later on."

Seems like good advice to me.
I'm bringing back Fisher, Marantz, HH Scott, McIntosh equipment brands that are up to 40 years old vintage.

With tubes inserted that I'm confident that are good I connect several voltmeters connected to each bias pot or resistor to make sure that none of tubes will significantly drop or increase bias current during voltage increments. There's a slight risk of damaging tubes, but it's part of business give or take. Blind replacement of DC supply caps (assuming they're all bad) before-hand usually never hurts and prevents from tubes being destroyed especially when I'm dealing with client's equipment that needed be restored.

Old coupling caps usually create less of a problem if any. quick test for short is usually enough

Now about increments and waiting time. I don't think that it's necessary to wait 30min per 6V increments. If I did that, I'd have to charge client at least a grand or couple depending on unit complexity and keep unit for a month or couple. I simply slowly bring it to the point when something begins to fail or to the operational voltage AFTER REPLACING ALL DC CAPS. Voltmeters or DMM testers I connect to each tube bias pot or if self-biased to the bias resistor to measure proper voltage. From voltage as you know you can figure the current and if you can't you'll need to go via basics of electrical circuits.
Current = Voltage/Resistance

Similar methods I apply to the vintage solid state equipment. I would usually use NTE replacement transistors instead of original or NOS to run these tests. I wouldn't be worried if I fry $1 worth power transistor instead of $15 one.
Lots of good, albeit varying, advice. My technique was based on the recommendation of a well known manufacturer who's name I have forgotten. I will say that technique is not one you would want to pay someone to do, but then if you are paying someone they will use what works for them. Given the amount of time these units were stored extra caution is certainly advised!
There is a simple way to do this using an incandescent light bulb. You remove all tubes and put the light bulb in series with the AC power and turn it on.

The light bulb will light up, which means most of the power is being dissipated by the bulb because the caps are likely shorted. However, if they need to 'form up', the bulb prevents them from heating up by limiting the current. If the bulb goes out the caps are formed up and OK.

Time-honored technique BTW; but if this is an amplifier you intend to really play a lot don't screw around- just change out every filter cap in sight... If there is a selenium rectifier change that out too.
If using a variac on a unit with the tubes installed care needs to be taken if the item is tube rectified.

If it has a slow start rectifier installed it will NOT see a slow ramp up from the variac, but will eventually quickly see higher voltage, which is not good for reforming caps.

There are some quick start subs for a GZ34 (think I once used a 5Y3, but not certain as it's been awhile).

A local tech once used a SS (plug in) rectifier on one of my vintage amps with a GZ34 (he made made it in a manner of minutes), but I've seen them for sale online as well.
With tube rectifier things get simpler because tube rectifiers reach operational voltage slow enough to catch problem with or even without variac.
With variac set to operational voltage and voltmeters attached to the bias pots or resistors and one attached to the rectifier output you can monitor gradual voltage increase. Once bias on any of the bias pots goes beyond tolerant, you can bring back variac to the noted voltage or below or turn amp off and inspect circuit elements around the fault bias pot or resistor.

Your advice does nor gell with the tech that worked on my Pilot 232, nor the advice I received from the AA forums.

Basically I was told that a GZ34 will not start to pass current until it reaches 80-90 VAC (which is 4-5 times higher than one wants to start when reforming lytics).
Dekay I mentioned earlier replacing all DC supply caps before even getting onto the variac.

Also forgot to mention that if using a 5Y3 (in place of a GZ34) it needs to be replaced with the proper tube once you get up to higher voltages (very important point left out).

Sorry, didn't notice the DC cap info.

I once used the light bulb method (think it was on a Pilot 240) and it worked well.
In my environment I have to pay rent and make sure that investment in rent is returned. Mostly I restore items I purchased from estates or items purchased in bulk by pound.
Replacing DC caps takes me less than hour on most tube units.