There are two general approaches. One is to use code in the MouseUp event of the radio buttons to assign a value to a field. The simplest would be:
getField("text1").value = (event.target.value !== "Off") ? "Hello" : "";
The other is to set up the text field as a calculated field, and do something like the following in the field's Calculate event:
event.value = (getField("radio1).value !== "Off") ? "Hello" : "";
The last script does not attempt to see which radio button was selected due to your "other than its own value" stipulation, but you should get the idea.