You should use # as href and the onclick event. Like so. Otherwise your javascript is correct.
Here is a working fiddle http://jsfiddle.net/FL7G8/1/
<a id="userName" href="#" onclick="showEditTextBox(this.id)">userName</a>
<a id="occupation" href="#" onclick="showEditTextBox(this.id)">occupation</a>
<a id="country" href="#" onclick="showEditTextBox(this.id)">country</a>
<a id="industry" href="#" onclick="showEditTextBox(this.id)">industry</a>
A cool effect would be to have href="#editHeader" for your anchor tags so that the window jumps to the element you are trying to change like so
<a id="industry" href="#editHeader" onclick="showEditTextBox(this.id)">industry</a>