Registration Plugin is what you are looking for. :)
UPDATED
In Case you want to have custom form. You would have to take permission from user and get his details. You can use following Code : 
<div id="fb-root"></div> 
<script src="https://connect.facebook.net/en_US/all.js"></script> 
FB.init({appId: 'XXXXXXXXXXXXX',status : true,xfbml  : true, cookie: true ,oauth  : true});
function login(){
        FB.getLoginStatus(function(response) {
        // checks if user already authorized
                    if (response.status === 'connected') {
                            FB.api('me?fields=id,name,email', function(user) {
                                     if(user != null) {
                                                                username  = user.name;
                                                                uid = user.id;
                                                                email = user.email;
                                                            }
                                });
                    } else {
        // If user is not authorized call FB.login for pop up window for authorization  , scope defines list of persmission requested with user
                    FB.login(function(response) {
                            if (response.authResponse.accessToken) {    
                                            FB.api('me?fields=id,name,email', function(user) {
                                                    if(user != null) {
                                                                username  = user.name;
                                                                uid = user.id;
                                                                email = user.email;
                                                            }
                                                        }) 
                                                    } 
                                                }, {scope:'email'});
                    }
                });
    }
You call login() at the press of your button.