How do you move your music within itunes from your regular library to the homeshares library so that you can import it to your new computer?

You do not have to move it as such. Here are the steps to setup HomeSharing

1) Ctrl B to turn on the top menu

2) File > Home Sharing > Create Home Share enter your apple id and password, click create

3) repeat steps 1 and 2 for the other computer and create home share using the same apple id and password

On your new machine if you have turned on the left hand sidebar the Shared Library should be about halfway down like this.

Select the songs you want and click import at the bottom right. If you want all songs then I would select one song nad Ctrl A to select all

Finally if you have a lot of songs to transfer Switch off the wifi on the old computer. Leave the wifi on the new one. Connect with an ehternet network cable. The copying speed is way faster.

Click import and grab a coffee

I would try switching itunes off and on on both machines and forcing it to reindex. Then when you click on your old computer library from within the itunes on your new machine you should see the songs as per my picture.

You do not need to drag and drop any songs anywhere

Try closing itunes on the old machine and restarting it. Then on your new machine reslect the old library and that should have refreshed the list.

After that if it still doesn't work try the troubleshooting article

http://support.apple.com/kb/TS2972?viewlocale=en_US&locale=en_US