You can use from bellow code:
1) Add selected Item from SourceListBox to TargetListBox
private void AddButton_Click(object sender, EventArgs e)
2) Remove selected Item from ListBox:
private void RemoveButton_Click(object sender, EventArgs e)
if (this.ListBox.SelectedItem == null)
3) Delete All items of ListBox:
private void RemoveAllButton_Click(object sender, EventArgs e)
4) for getting data from Database you can attend to my answer to similar question in bellow link:
Connectivity of only column from database
I hope it's helpful.
..If it's helpful for you please accept it and give Up vote..