C# How do I click a button by hitting Enter whilst textbox has focus?

The simple option is just to set the forms's AcceptButton to the button you want pressed (usually "OK" etc):

    TextBox tb = new TextBox();
    Button btn = new Button { Dock = DockStyle.Bottom };
    btn.Click += delegate { Debug.WriteLine("Submit: " + tb.Text); };
    Application.Run(new Form { AcceptButton = btn, Controls = { tb, btn } });

If this isn't an option, you can look at the KeyDown event etc, but that is more work...

    TextBox tb = new TextBox();
    Button btn = new Button { Dock = DockStyle.Bottom };
    btn.Click += delegate { Debug.WriteLine("Submit: " + tb.Text); };
    tb.KeyDown += (sender,args) => {
        if (args.KeyCode == Keys.Return)
        {
            btn.PerformClick();
        }
    };
    Application.Run(new Form { Controls = { tb, btn } });

The usual way to do this is to set the Form's AcceptButton to the button you want "clicked". You can do this either in the VS designer or in code and the AcceptButton can be changed at any time.

This may or may not be applicable to your situation, but I have used this in conjunction with GotFocus events for different TextBoxes on my form to enable different behavior based on where the user hit Enter. For example:

void TextBox1_GotFocus(object sender, EventArgs e)
{
    this.AcceptButton = ProcessTextBox1;
}

void TextBox2_GotFocus(object sender, EventArgs e)
{
    this.AcceptButton = ProcessTextBox2;
}

One thing to be careful of when using this method is that you don't leave the AcceptButton set to ProcessTextBox1 when TextBox3 becomes focused. I would recommend using either the LostFocus event on the TextBoxes that set the AcceptButton, or create a GotFocus method that all of the controls that don't use a specific AcceptButton call.

The TextBox wasn't receiving the enter key at all in my situation. The first thing I tried was changing the enter key into an input key, but I was still getting the system beep when enter was pressed. So, I subclassed and overrode the ProcessDialogKey() method and sent my own event that I could bind the click handler to.

public class EnterTextBox : TextBox
{
    [Browsable(true), EditorBrowsable]
    public event EventHandler EnterKeyPressed;

    protected override bool ProcessDialogKey(Keys keyData)
    {
        if (keyData == Keys.Enter)
        {
            EnterKeyPressed?.Invoke(this, EventArgs.Empty);
            return true;
        }
        return base.ProcessDialogKey(keyData);
    }
}

private void textBox1_KeyPress(object sender, KeyPressEventArgs e)
{
    if (e.KeyChar == '\r')
    {
        button1_Click(textBox1.Focus(),e);
    }  
}