When saving a monitor profile, your X-Rite/Monaco application will set it as the default for the active display. In most cases you need do nothing further with it. To confirm that the profile is assigned to the display, do the following:
On MacOS X, go to System Preferences>Displays and click on the Color tab for the monitor in question. The active profile for that display will be highlighted in the list.
On Windows, go to Display Properties> Settings and highlight the monitor in question. Click the Advanced button and choose the Color Management button. The active profile for that display will be listed next to Default monitor profile:
Most color management savvy applications will automatically detect the active display profile and use it for rendering to the display. Adobe applications, like Photoshop will do this. You can confirm that it is being used by going to Color Settings and looking in the list of RGB Working Spaces. The active profile for you display should be listed next to "Monitor RGB -".
Other applications may require you to manually select the proper display profile. Be sure to review the documentation provided with your software to make sure it is making the most of your profiles.