A bit late to the party, but I hope not too late. I work as a color management technician, specifically in printing - more specifically in offset lithography, so I wouldn't call myself an expert, but I've done a fair amount of measurements and fiddling with knobs and buttons.
Calibrating computer displays is totally different from calibrating TV sets. Modern operating systems use icc profiles for correcting displayed colors. Icc profiles can be generated by
characterizing the display (measuring the responses of a set of known RGB input values with a colorimeter and/or spectroradiometer). To get a good icc profile a preliminary
calibration is highly recommended - this will linearize the RGB gamma curves (or set the desired gamma curve depending on your use case), set the correct white and black points, etc. It is important to note that any change in display settings (brightness, contrast, backlight level) or changes which develop with aging will require a new calibration and characterization.
For the best results, I use both an X-rite i1Pro (rev E.) spectro and an i1 DisplayPro colorimeter and the excellent and free
DisplayCal tool (based on
Argyllcms). You'll find much more information and you can become an expert if you read through these sites.
For quick calibration I just use the i1Pro and i1Profiler (not free) and a small testchart - it's usually good enough for me as I don't do retouching.
For professional work, we recommend Eizo CG/CX monitors with built-in hardware calibration and a colorimeter. You just press a button and after 2 minutes you have a calibrated monitor.
For TV calibration there is also a free tool called
HCFR (also based on Argyllcms). Since you can't load an icc profile to TV, you have to dial-in the correct values of your preferred standard (sRGB, Rec. BT709, DCI-P3, etc.) starting with White Point and then the correct R,G,B,C,M and Y coordinates followed by Gray balance and Gamma (again as defined in the standard). Depending on your display type and technology the methods and nuances will be wildly different but one can always ask for help either on Argyllcms or AVS forums.