You can still pass in callbacks to them. So if I got the parent's intent right, you've got:

  function bunchOfAsyncThings(callback) {
    var function1, function2;
  
    function1 = function (callback) {
      // do stuff here, then do callback
      function2(callback);
    };
    
    function 2 = function (callback) {
      // done with everything
      callback();
    };
   
    function1(callback);
  }

(Edit: formatting)