OK, the first thing to know is that you can always send it to Ed and get it fixed, if you have to. I say that not to get you to send it, but so you won't panic. :^) There is another option - if there is a Bottlehead near you, they might be willing to help. We're a pretty tight community.
Yes, the care and feeding of a home-built amp is likely to require a meter at some point, might as well be now. Cheap ones are good enough for most people and are widely available. Make sure you can measure up to 500 volts DC, and resistances.
Did you get the manual? There is a section on safety there which you MUST read and understand before you start poking your fingers in where there might be the aforementioned 500 volts. There is also a section on troubleshooting in the manual. And, if you are going to do any of your own troubleshooting, or if anyone here is going to be able to help you, you will have to become acquainted with the terminal identifications, also made clear in the manual. If you don't have it, either bug the seller or contact Eileen and get it.
OK, now we know a few things. The tubes glowed at first, so the transformer and tube heater power supply are working. The quick fade sounds like the fuse blew; you can check the fuse and may be able to tell visually if that happened. If not, you can measure the resistance when you have a meter and confirm that.
Assuming the fuse blew, and knowing that the tubes lit up, (and it worked for a few months), we're left with a guess that something in the high voltage areas shorted out. The burning smell is another clue. So you can at least turn it over and look closely at every part to see if there are charred remains of any dead parts. Learn to recognize resistors and capacitors, and look for bulging capacitors as well as burnt resistors.
Well, there's a starting point anyhow.