add textbox by click on linklabel c#

First, in the Visual Studio Form Designer, double-click on the LinkLabel. Now, an event handler to the LinkClicked method is created, and now, you can edit the code of the yourLinkLabel_LinkClicked method:

private void linkLabel1_LinkClicked(object sender, LinkLabelLinkClickedEventArgs e)
{
    yourTextBox.Visible = true;
}

[Edit]

If you want to make the text box invisible when clicking a second time, try this:

private void linkLabel1_LinkClicked(object sender, LinkLabelLinkClickedEventArgs e)
{
    yourTextBox.Visible = !yourTextBox.Visible;
}