Set up your ListView to have an event handler for the KeyDown event. Then check that the key that was pressed was the delete key. Then use SelectedItems to see which items are selected and remove them. Make sure to go from the bottom up because your SelectedItems collection will be constantly changing.
private void listView1_KeyDown(object sender, KeyEventArgs e)
{
if (e.KeyData == Keys.Delete)
{
for (int i = listView1.SelectedItems.Count - 1; i >= 0; i--)
{
ListViewItem li = listView1.SelectedItems[i];
listView1.Items.Remove(li);
}
}
}