I, for one, would appreciate a clear and thorough explanation (bonus points if presented in a non-condescending manner) for the thought process and procedures one goes through when calibrating a monitor for individual papers.
... depends a bit on the hardware (monitor & measurment device) and software (calibration software and also image editing software).
The most critical part in all that is "paper white" IMHO. First: your perception of "paper white" depends on the viewing conditions... so the "ambient" light you are using to compare your monitor and your print is critical. This is why viewing boothes are useful (and of course ideally the entire room you are working in should be suited to do color critical work...). If you don't have contolled lighting for image editing/softproofing you should try to create an environment that comes as close as possible to said ideal. And the "ambient"-light should be fairly reproduceable.
Secondly: measurement devices "see" paper white" different than we humans do. Worst case is papers containing optical brighteners measured without UV-cut filter... in this case the measured "white" is actually "blue" (and since it's blue it's also much too dark as a reference).
To overcome non-ideal viewing conditions and "wrong" white points in paper profiles you can softproof without "paper-white" simulation enabled:
1- calibrate your display to match your preferred paper (both whitepoint and luminance) visually. Depending on your monitor & calibration software you can adjust the luminance and white point manually within the software ... otherwise you can use the luminance setting and the RGB-Gain of your display.
2- it's very hard to adjust the white point visually with pure white. Use a print of your prefered paper containing white and different grey patches...
3- softproof settings in Photoshop: set Photoshop's background to white. Softproof dialogue: Rendering Intend: perceptual or rel. colormetric. For the preview
disable "paper white simulation" (since your monitor already matches the white point and luminance of your paper the simulation of paper white is not needed anymore). But
enable "black ink" simulation so that the actual contrast range of the paper is taken into account.
This approach is not ideal either. But it takes out misleading white points in paper profiles out of the equation.