+1 on everything mentioned here so far.
Here are important things I would add concerning tube amp construction:
Don't smoke weed, drink, or otherwise get loaded and try to build an amp. I used to party. A lot. Then I started building amps. Make a clear distinction between work time and recreation time if you are not going to give up partying.
Make sure you understand the schematic vs. the layout. It is important to try and see how everything relates so when you go to build it the underboard wires make sense (there are a dozen on Weber's 5E3 layout) and you get clean lead dress inside the amp.
It doesn't get dangerous until you fire it up and have the open chassis in front of you. Remember to keep your left hand in your jeans pocket at all times when you are probing around inside the amp and checking voltages. If the worst happens you don't want to get 300+VDC across your ticker.
Use a plain wood chopstick for probing around an amp, you are probably going to have to shift wires around a bit to get the least amount of noise/hum. Don't use a pencil, your finger, or any other protruding fleshy body part, ever.
Always, always, always treat the filter caps and other electrolytic caps as if they were are charged, even if the amp is unplugged and has been sitting for months, and discharge them properly always! Always! Weber sells a snuffer stick for $15 that does the job well. I use a Mac technician discharge tool for discharging CRT's the can have 20k volts stored in them. It doesn't have an internal resistor so it makes a great whip-crack sound when you discharge that much!
If something isn't working right unplug the amp and observe the suggestion above after walking away for 10 minutes to think about what might be going on.
Watch the way this guy Gabi wires up the power supply on this 18watt clone. He has alot of great common sense tips if you can sit through the lengthy and talkative videos, in part 3 he shows how to do the heaters cleanly. He is a super great guy too.
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Read as much as possible. PPwatt.com is a great resource for 5E3 builds.
Keep in mind that amps are actually alot simpler than many stompboxes and easier to build because of the ample room inside your average chassis.
Once you get everything up and running play the thing for 20-30 hours to get the speaker broken in and the coupling caps burned in. Then fall in love with it. I run my ipod through every amp I build for the first 10 hours or so after I am satisfied that the construction has gone well.