You could either access the element’s value by its name:
document.getElementsByName("textbox1"); // returns a list of elements with name="textbox1"
document.getElementsByName("textbox1")[0] // returns the first element in DOM with name="textbox1"
So:
<input name="buttonExecute" onclick="execute(document.getElementsByName('textbox1')[0].value)" type="button" value="Execute" />
Or you assign an ID to the element that then identifies it and you can access it with getElementById
:
<input name="textbox1" id="textbox1" type="text" />
<input name="buttonExecute" onclick="execute(document.getElementById('textbox1').value)" type="button" value="Execute" />