You buy a monitor calibration device. You calibrate your monitor. Then what?
Not a thing. The monitor profile just sits deep in your operating system, where Photoshop and your other colour-managed programs know where to find it and refer to it. As the owner of the computer, your only task is to recalibrate regularly to make sure the profile is up-to-date.
Too many people get into trouble by setting their monitor profile as their Working Space, or assigning it to their images, or soft-proofing with it. None of those things are necessary, and all of those thing will end in tears.
Just leave it alone!
That is all.