If you are looking for something like below
Listbox1 ListBox2
1 a
2 b
3 c
Now you have button one >> and button two <<
on button one(>>) click item should go in Listbox2
On button two(<<) click item should go in Listbox1
If you are having trouble in listbox after moving, you need to show datasource to Listbox.
something like below
Items.Add("something");
Listbox1.Datasource=Items;
let me know if you are having problems