You will need to delete things that are taking up more space. Apps aren't usually taking up much space, but if you have videos and music on your iPhone then that will be the space users. Not sure what GB you have but it looks like you will need to delete some of the music and/or videos if you want to add music to your iPhone. Also, if you have a lot of photos then you might need to consider deleting those after backing them up on your computer or elsewhere so you can free up some space. For those with low GB iPhones this is an issue that unfortunately you discover after it's too late to do anything about it (since we can't add SD cards to upgrade storage space). That's why many people go by the rule of it's better to have more GB than you think you will use than to find out later you should have went with a bigger size. Of course, you'll have those iPhone haters that will gladly point out that is why iPhones are terrible because you can't upgrade the capacity with an SD card.
If you want to delete apps u press an app and click the x. In iTunes you can select what music u want that day or whatever. You can check what u want and go into sync settings there should be an option to sync only checked songs. Same with apps you can pick which ones u want. You do this when you click your phone in iTunes.