I've worked on 3 different Atari games, so maybe my GUESSING here will be relevant:
First, check all fuses (and fuse holders)
Next, the board should have little metal loops sticking out of it all over the place. These are test points. They will have labels printed next to them. All you need to do is test voltage at those points. You place one test probe to a point marked "GND" and the other to one marked with a voltage value. THe ones you want to test will likely be +5v, +12v, and/or +22 . If any of these are off by more than 1 +or- then the voltage on the AR-II board must be adjusted or the AR-II board needs repair.
The AR-II board will also have test points on it. But be careful... Some of them are AC, so make sure you set your meter to correct measuring setting.
That's about it really. If your game board shows "normal" readings for +5 and the +12, then your power is good. Check your TEST SWITCH (usually next to the volume knob). Place the test switch into "on" position and you will hear beeps if your game board is not working correctly. (Download the Tempest manual to find out about the Test Mode).