Press enter in textbox to and execute button command

You could register to the KeyDown-Event of the Textbox, look if the pressed key is Enter and then execute the EventHandler of the button:

private void buttonTest_Click(object sender, EventArgs e)
{
    MessageBox.Show("Hello World");
}

private void textBoxTest_KeyDown(object sender, KeyEventArgs e)
{
    if (e.KeyCode == Keys.Enter)
    {
        buttonTest_Click(this, new EventArgs());
    }
}

Alternatively, you could set the .AcceptButton property of your form. Enter will automcatically create a click event.

this.AcceptButton = this.buttonSearch;