Changing this line (line 21, over function):

$$.showSuperfishUl().siblings().hideSuperfishUl();

To this:

$$.click(function(){$(this).showSuperfishUl().siblings().hideSuperfishUl();});

Full superfish code for clicking the menu:

/*

 * Superfish v1.4.8 - jQuery menu widget

 * Copyright (c) 2008 Joel Birch

 *

 * Dual licensed under the MIT and GPL licenses:

 *  http://www.opensource.org/licenses/mit-license.php

 *  http://www.gnu.org/licenses/gpl.html

 *

 * CHANGELOG: http://users.tpg.com.au/j_birch/plugins/superfish/changelog.txt

 */



;(function($){

    $.fn.superfish = function(op){



        var sf = $.fn.superfish,

            c = sf.c,

            $arrow = $(['<span class=',c.arrowClass,'> &#187;</span>'].join('')),

            over = function(){

                var $$ = $(this), menu = getMenu($$);

                clearTimeout(menu.sfTimer);

                $$.click(function(){$(this).showSuperfishUl().siblings().hideSuperfishUl();});

            },

            out = function(){

                var $$ = $(this), menu = getMenu($$), o = sf.op;

                clearTimeout(menu.sfTimer);

                menu.sfTimer=setTimeout(function(){

                    o.retainPath=($.inArray($$[0],o.$path)>-1);

                    $$.hideSuperfishUl();

                    if (o.$path.length && $$.parents(['li.',o.hoverClass].join('')).length<1){over.call(o.$path);}

                },o.delay); 

            },

            getMenu = function($menu){

                var menu = $menu.parents(['ul.',c.menuClass,':first'].join(''))[0];

                sf.op = sf.o[menu.serial];

                return menu;

            },

            addArrow = function($a){ $a.addClass(c.anchorClass).append($arrow.clone()); };



        return this.each(function() {

            var s = this.serial = sf.o.length;

            var o = $.extend({},sf.defaults,op);

            o.$path = $('li.'+o.pathClass,this).slice(0,o.pathLevels).each(function(){

                $(this).addClass([o.hoverClass,c.bcClass].join(' '))

                    .filter('li:has(ul)').removeClass(o.pathClass);

            });

            sf.o[s] = sf.op = o;



            $('li:has(ul)',this)[($.fn.hoverIntent && !o.disableHI) ? 'hoverIntent' : 'hover'](over,out).each(function() {

                if (o.autoArrows) addArrow( $('>a:first-child',this) );

            })

            .not('.'+c.bcClass)

                .hideSuperfishUl();



            var $a = $('a',this);

            $a.each(function(i){

                var $li = $a.eq(i).parents('li');

                $a.eq(i).focus(function(){over.call($li);}).blur(function(){out.call($li);});

            });

            o.onInit.call(this);



        }).each(function() {

            var menuClasses = [c.menuClass];

            if (sf.op.dropShadows  && !($.browser.msie && $.browser.version < 7)) menuClasses.push(c.shadowClass);

            $(this).addClass(menuClasses.join(' '));

        });

    };



    var sf = $.fn.superfish;

    sf.o = [];

    sf.op = {};

    sf.IE7fix = function(){

        var o = sf.op;

        if ($.browser.msie && $.browser.version > 6 && o.dropShadows && o.animation.opacity!=undefined)

            this.toggleClass(sf.c.shadowClass+'-off');

        };

    sf.c = {

        bcClass     : 'sf-breadcrumb',

        menuClass   : 'sf-js-enabled',

        anchorClass : 'sf-with-ul',

        arrowClass  : 'sf-sub-indicator',

        shadowClass : 'sf-shadow'

    };

    sf.defaults = {

        hoverClass  : 'sfHover',

        pathClass   : 'overideThisToUse',

        pathLevels  : 1,

        delay       : 200,

        animation   : {opacity:'show'},

        speed       : 'fast',

        autoArrows  : true,

        dropShadows : true,

        disableHI   : false,        // true disables hoverIntent detection

        onInit      : function(){}, // callback functions

        onBeforeShow: function(){},

        onShow      : function(){},

        onHide      : function(){}

    };

    $.fn.extend({

        hideSuperfishUl : function(){

            var o = sf.op,

                not = (o.retainPath===true) ? o.$path : '';

            o.retainPath = false;

            var $ul = $(['li.',o.hoverClass].join(''),this).add(this).not(not).removeClass(o.hoverClass)

                    .find('>ul').hide().css('visibility','hidden');

            o.onHide.call($ul);

            return this;

        },

        showSuperfishUl : function(){

            var o = sf.op,

                sh = sf.c.shadowClass+'-off',

                $ul = this.addClass(o.hoverClass)

                    .find('>ul:hidden').css('visibility','visible');

            sf.IE7fix.call($ul);

            o.onBeforeShow.call($ul);

            $ul.animate(o.animation,o.speed,function(){ sf.IE7fix.call($ul); o.onShow.call($ul); });

            return this;

        }

    });



})(jQuery);