The getElementById('xxxxx').setText('')
approach was the right way to do it. but the way you tried to test it doesn't work... the new value would only be available in the next handler call.
/*
This function only has the desired effect if it is called within the handler
function (not within a nested function in the handler function).
*/
function restartGUI() {
var gui = UiApp.getActiveApplication();
gui.getElementById('equipmentIDField1').setText('');
gui.getElementById('equipmentIDField2').setText('');
gui.getElementById('equipmentIDField3').setText('');
gui.getElementById('studentLastNameField').setText('');
gui.getElementById('labasstLastNameField').setText('');
return gui;
}