This is the manual way, in case sync doesn't work for you. First, download the songs to your computer. Once your phone is connected via USB, you can go to My Computer and double click the drive letter that represents your phone as a mass storage device. This will open a window showing any folders and files on your phone. You can copy and paste files to these folders like you would any other drive or storage device. OR First connect your phone. Then tell your browser to download the music files directly to your phone.
When you download items, they go into a folder and from there, you have to sync them so they will transfer the items you download onto your phone.