Once the manually manage option is checked and it has synced up you are ready to go. Keep in mind that this is the only time the iPhone will sync, once it's done you will be able to manually pick and choose your songs and videos you want on your iPhone.
So the hard part is done. You should now have the manually manage music and video box checked. From here you can click on the music option on the left side under the Library section. You then will just click on a song and simply drag it to your iPhone. You should
see a a little green plus icon pop up as the song hovers over the iPhone. When you release the mouse, it will be added to the iPhone. That's all you got to do.
Now if you would like to remove an item from your iPhone it's just as simple. Make sure your iPhone is plugged in and click on the music option that is located under your iPhone. Go and select the song you want to remove and just click the delete button on your keyboard. That's all that needs to be done. You will see the file disappear and it is no longer on your iPhone.
Now you are only able to sync your iPhone to one iTunes library, so every time you plug an iPhone into a different computer then you will have to erase and sync your iPhone so it will only remain to not sync if you keep using the same iTunes library.
This feature makes it a little easier to maintain the space on your iPhone for what you want so take advantage of it and enjoy. Check out a guide about deleting iPhone apps from your iPhone to save even more space.