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
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