Assuming that you are using SNOW default forms and using client script, you are trying to add "options" to dropdowns, here is an example, which will add options to a control "u_category".

Note: I am assuming the response returned by your API/Web service is already in JSON format. If not, Please copy that response here. I put few alert statements for debugging. Remove them later, once you get it working.

ClientScript:

function onLoad() {

     //Type appropriate comment here, and begin script below

var ga = new GlideAjax('Test');

ga.addParam('sysparm_name','getCategories');

ga.getXML(getCategoriesOutput);

} 

function getCategoriesOutput(response) {

     var answer = response.responseXML.documentElement.getAttribute("answer");

   alert(answer);

     var objJSON = JSON.parse(answer);

   for(var loop = 0 ; loop < objJSON.categories.length;loop++)

   {

   alert(objJSON.categories[loop].Name);

   g_form.addOption('u_category',objJSON.categories[loop].Value,objJSON.categories[loop].Name);

   }

}

Server-side script include

var Test = Class.create();

Test.prototype = Object.extendsObject(AbstractAjaxProcessor, {

 getCategories: function()

   {

   try {

   /*var r = new sn_ws.RESTMessageV2('x_equi2_trouble_ti.Trouble Ticket Post', 'post');

   var response = r.execute();

   var responseBody = response.getBody();

   var httpStatus = response.getStatusCode();

   return responseBody;*/

   return '{\"categories\":[{\"Name":\"John\", \"Value\":\"Doe\"}, {\"Name":\"Anna\", \"Value\":\"Smith\"},{\"Name":\"Peter\", \"Value\":\"Jones\"}]}';

   }

   catch(ex) {

   var message = ex.getMessage();

   return "";

   }

   },

       type: 'Test'

});