There's two steps :

1. Add a new event handler to the CellDoubleClick event of your datagrid :

dataGridView1.CellDoubleClick += new
System.Windows.Forms.DataGridViewCellEventHandler(this.dataGridView1_CellDoubleClick);

2. Create the event handler method dataGridView1_CellDoubleClick

private void dataGridView1_CellDoubleClick(object sender,
DataGridViewCellEventArgs e)
{
   if (e.ColumnIndex == 3)
       // TODO
}

Using the column index is not a good solutin, you can get the instance of
the DataGridViewColumn from the Columns property of your DataGrid like this :
dataGridView1.Columns["MyColumn"]
and then use the Index property of the returned column.