The process is similar to screen calibration except that the output is one step removed.

Most products use a software to output a controlled test which is basically a grid of colors. A hardware spectrograph that looks at each square and sends the result back to the calibration software is also needed. This creates a multi-dimensional matrix to map between the output and input color spaces.

This has to be done for each combination of printer and paper type, usually with a 24 hours waiting period between the printing step and the spectrograph, to take into account changes as ink dries.

HP is the only consumer-level manufacturer to offer printers with a spectrograph built-in. This lets the printer output the patch, measure the results and even correct for incremental drift.

Due to the cost of these calibration solution, you can even calibrate a printer by proxy. To do that you are given a patch that you print and mail it to the calibration service provider. They scan the results with their spectrograph and send you back a profile for a fee (About $150 CDN last time for me). This profile is valid for the printer, paper and ambient humidity (!) corresponding to when the patch was printed.