The reason it doesn't work, as already mentioned, is that your methods don't handle the callbacks you pass in as arguments.
To make it work like you want you need to rewrite your methods to look like this:
function getOne(callback)
{
callback("one");
}
function getTwo(callback)
{
callback("two");
}
Since you question is about function execution synchronization however, you might wish to go down another path.
What you are doing will work fine for a couple of functions, but when you get to the point where you wish to synchronize many functions you end up with the pyramid of doom where code marches to the right faster than it marches forward.
step1(function (value1) {
step2(value1, function(value2) {
step3(value2, function(value3) {
step4(value3, function(value4) {
...continue ad nauseum
});
});
});
});
In that case you might want to look into futures and promises
You can read more about promise patterns in javascript here:
http://www.html5rocks.com/en/tutorials/es6/promises/
getOnedoesn't take parameters. How can you possibly expect your callbacks you're passing into them to be called?