Here's how you do it. If you have not yet installed the drivers for your phone, do that first. Then you plug your phone into your computer via the sync cord. An AutoPlay option should pop up giving you four choices of things you can do. You want to click the option with the folder icon by it (on mine it was the third), the one that says open device to view files using Windows Explorer. When you click on this option, the only place you can continue is a link that says Internal Storage. Click on that link and you will be taken to a screen with various folders (and some other misc papers). You can open any of these folders to see the music on your phone. I chose to open the Music folder because that way it is sorted by artist. Every artist has a folder with your songs in it. Right click the folder (or folders) you want deleted and click the delete option. You can also select just specific songs you want deleted by further exploring the folder of your choice.
If the AutoPlay option does not pop us first, you can also get to the internal storage screen by going to My Computer and clicking of the Sumsung Juke link under the Portable Devices headline. The you can just follow the instructions above from the Internal Storage part.
Hope this helps!!!