How do I save a gradient to the Library?

I you first save your gradient to your swatches panel, it will be automatically added there in new documents if you follow these steps.

Global colors, gradients and pattern swatches are not supported in CC libraries.

But as a workaround you can drag an object filled with a pattern/gradient/global color to the CC Library 

You can also drag multiple items filled with different patterns/gradients/global colors together into a CC library to simulate a library.

The easiest way to add them to a new document is to hold down the Alt key when you drag them from the library and place them in a new document. The patterns/gradients/global colors automatically get added to your swatches panel.

You can hit escape before you click to place the object(s) or delete the dragged library items because the swatches are now part of the document.