First of all, with most modern components and operating systems and software, if you install them correctly, then all of the profiles will kind of fall into place, and it works. However, if you have any single piece whose profile isn't right, or if the OS can't find the profile, or the software can't deal with it, then you have a problem. Anyway, it is supposed to work right in theory.
If you have a problem, or old components, or if you need to be ultra-precise, then you can use the external systems like a color spyder.
I can take a color input target, scan it in, and it looks the same on my monitor. Then I can print it out on my Epson printer, and the output looks the same as the input target. I call that calibrated.
Then I can shoot with my Canon camera, suck that in as RAW, convert to TIF, make one gamma correction, and then I am still correct. I leave that gamma correction number conveniently stuck in my image editor program.
Mine is probably only 99.9% perfect, but nobody has yet called me about any problem.
---Bob Gross---