Call a function after previous function is complete

Specify an anonymous callback, and make function1 accept it:

$('a.button').click(function(){
    if (condition == 'true'){
        function1(someVariable, function() {
          function2(someOtherVariable);
        });
    }
    else {
        doThis(someVariable);
    }
});


function function1(param, callback) {
  ...do stuff
  callback();
} 

Try this :

function method1(){
   // some code

}

function method2(){
   // some code
}

$.ajax({
   url:method1(),
   success:function(){
   method2();
}
})

This answer uses promises, a JavaScript feature of the ECMAScript 6 standard. If your target platform does not support promises, polyfill it with PromiseJs.

Promises are a new (and a lot better) way to handle asynchronous operations in JavaScript:

$('a.button').click(function(){
    if (condition == 'true'){
        function1(someVariable).then(function() {
            //this function is executed after function1
            function2(someOtherVariable);
        });
    }
    else {
        doThis(someVariable);
    }
});


function function1(param, callback) {
    return new Promise(function (fulfill, reject){
        //do stuff
        fulfill(result); //if the action succeeded
        reject(error); //if the action did not succeed
    });
} 

This may seem like a significant overhead for this simple example, but for more complex code it is far better than using callbacks. You can easily chain multiple asynchronous calls using multiple then statements:

function1(someVariable).then(function() {
    function2(someOtherVariable);
}).then(function() {
    function3();
});

You can also wrap jQuery deferrds easily (which are returned from $.ajax calls):

Promise.resolve($.ajax(...params...)).then(function(result) {
    //whatever you want to do after the request
});

As @charlietfl noted, the jqXHR object returned by $.ajax() implements the Promise interface. So it is not actually necessary to wrap it in a Promise, it can be used directly:

$.ajax(...params...).then(function(result) {
    //whatever you want to do after the request
});

If you're using jQuery 1.5 you can use the new Deferreds pattern:

$('a.button').click(function(){
    if(condition == 'true'){
        $.when(function1()).then(function2());
    }
    else {
        doThis(someVariable);
    }
});

Edit: Updated blog link:

Rebecca Murphy had a great write-up on this here: http://rmurphey.com/blog/2010/12/25/deferreds-coming-to-jquery/