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();
} 

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/

Try this :

function method1(){
   // some code

}

function method2(){
   // some code
}

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