Best way to handle the error in async node
Check out promises. They are not (yet) available natively in Node.js, but you can use Q library.

Promises allow you to make your control flow explicit with methods like catch and finally instead of hiding it in callbacks.

Also you won't need async with promises.

Q provides a convenience method to “convert” a function that accepts a callback to a promise-returning function.

I don't understand what fnOne or fnTwo is your code (seemingly objects and not functions), so I can't really translate your example, but it would look similar to this:

var Q = require('q');

// Convert our functions to promise-returning functions
var getOne = Q.nbind(fnOne.GetOne, fnOne),
    getTwo = Q.nbind(fnTwo.two, fnTwo) ;

getOne(req, res)
  .then(function (result) {
    return getTwo(result);
  })
  .then(function (result) {
    // do something useful with final result
  })
  .catch(function (err) {
    console.error("Three was an error", err);    
    res.send("Error in serving request.");
  })
  .done();