1- The color temp of the monitor should be D65 (except in Japan and Asian countries). Sometimes this is labeled 6500K (which is not the same color as D65, but is pretty close).
In practice you want all the light sources in your room to be in the ballpark of D65, but more importantly they should all match. Your eye kind of auto white balances to what it's looking at... you don't want that to drift.
2- Display a black and white image on your monitor (actually de-saturate the image to ensure that it's perfectly black and white). Real world images converted to black and white are good. You can adjust the bias controls to try to get the color right.
3- When a CRT ages, its colors will shift... it may be bad enough that you can't get grayscale tracking to an acceptable level. In that case you need a new monitor.