Powering up a SET amp after 6 months in storage

What precautions do I have to use in turning on my SET amp after it has been sitting unused for a number of months? I have heard the phrase "bring the amp back up slowly" in connection with tube amps and preamps, but I don't know exactly what that means, and if a tech guy has to do this for me. FYI, the amp has a mute switch in the back if that is any help. Thanks.
To bring up slowly you need a variac which is basically a giant variable resistor. You start out at 10% of rated voltage and bring it up in 10% increments every 10 minutes or so. I believe this is primarily for the capacitors, but it is good for tubes too. Some tube electronics have soft start circuitry for the tubes just to avoid shocking them on every turn-on. Six months of storage is borderline for doing this, if you know a good tech who would do it for low cost it would be worth it, otherwise it's a judgement call.
Don't worry about it. Six months is nothing. Turn it on and enjoy.
Six months is hardly a long time to be idle. I would just remove and reinsert the tubes (or better, clean the tube pins and the socket) to assure good contact and then power the amp up.

The concern with long-term storage has mostly to do with electrolytic caps that have begun to dry out. These can be brought back to life, but it is best done by slowly powering the caps up. But, this is a concern after years of storage.

Also, if your amp utilizes tube rectification, power naturally comes up a bit more slowly than with solid state rectification, so capacitors are given less of a sudden jolt.
The issue with gear that has been sitting for long periods is generally a breakdown of the dielectric charge on the capacitors. To reform them, as pmotz suggests, a variac is used. Although initial power should actually be hundreths or even milliwatts and this power should be applied for at least 24 hours, increasing it slowly, over a period of days, to full power. But six months is just not a very long time though and there should be no issue whatsoever with just flipping the switch and enjoying the amp.
Agree 6 months is not a problem. Six YEARS... however, might be.
One way to do a poor imitation of proper care for a long term storage is to turn it on for only a moment. Less than a second. Some juice flows... but not enough to break anything. Then on again for two seconds after about five minutes. Then you are ready to go.