Globe storage

Globe storage is a glitch that allows the cutscene that normally plays when placing Cappy on the Odyssey's globe to be stored. Cappy will remain on the globe while Mario can freely traverse the kingdom, and upon loading the Odyssey (which is normally triggered by pointing the camera at it), the globe cutscene will play, meaning that Mario will be instantly teleported to the Odyssey.

Execution

To trigger globe storage, the Odyssey must be unloaded at the exact moment that Cappy latches onto the globe. The window for this to occur is commonly believed to be two frames.

In most cases, the Odyssey (and thus the globe) becomes unloaded when it is not within view of the camera and Mario is sufficiently far away from it. This means that in order to trigger globe storage, Cappy must latch onto the globe as the Odyssey leaves the screen, all while Mario is far enough away for the Odyssey to unload.

Normally, this would be very hard to reproduce, since it is difficult to control exactly when the Odyssey moves off-camera. However, it is much easier with the help of Snapshot Mode, which allows the camera to be rotated while the game is paused. The steps to execute the trick are as follows:

Jump and throw Cappy so that he is right next to, but not touching, the globe.
Turn around and dive away from the Odyssey while holding X or Y to keep Cappy extended. (To dive, use the other cap throw button.)
Roll boost without using motion controls (by pressing one of the cap throw buttons) to get even farther from the Odyssey.
Just before Cappy attempts to return to Mario, input a motion control shake to home Cappy onto the globe.
Immediately afterward, enter snapshot mode before Cappy touches the globe.
Use Snapshot Mode buffering to frame advance until Cappy latches onto the globe. In other words, exit snapshot mode and very quickly re-enter it to advance the game by a couple of frames, and repeat until Cappy appears to be attached to the globe.
Rotate the camera so that the Odyssey is no longer on screen, and then exit Snapshot Mode.

If performed correctly, Cappy will stay on the globe and not come back to Mario, but the globe cutscene will not trigger yet.