Q: How do I get my itunes library that is already on my iPhone onto my ipod shuffle fourth generation

It needs to go through iTunes on your computer, because that is the only way to sync songs to an iPod shuffle. 

If the songs on the iPhone were synced using iTunes on your computer, just use that same iTunes library to sync the same songs to your shuffle.

If you downloaded the songs from the iTunes Store directly on the iPhone, you can download previous purchases using iTunes on the computer at no cost.  In iTunes, sign in using the same Apple ID used on the iPhone.  On the iTunes Store Home page, click on Purchased under QUICK LINKS.  On the Purchased screen, you can find and download previous purchases made using your Apple ID, including purchases made on the iPhone.  Once those songs are in your iTunes library, you can sync them as desired to the shuffle.

If your situation is something else, please post back with more info.