Can't figure out how to remove select music from my iPhone 4 with the new iTunes

My old PC with all my music on iTunes died, and I need to remove some music from my iPhone 4 to make room for the new OS update. I downloaded iTunes on a different computer and tried to sync the iPhone to it, to move all the music on my iPhone to iTunes so I could deselect what songs I wanted to remove to make the storage space. I can't figure out how to do this with the new (non-user-friendly) iTunes update. When I sync the phone, the only songs that show up are the ones I have purchased on iTunes, but non of the songs/albums that I transfered from CDs. I don't want to reset my phone to delete ALL my music, just select songs/albums. Can anyone please help me figure out the new iTunes to be able to do this? It is driving me nuts and I'm getting really mad at Apple for their constant updates making things less easy to use!