Limit Joomla extensions
With beginning Joomla users there often is a tendency to install a lot of extensions, especially front-end extensions like galleries, social media feeds, video plugins, etc., because they look so nice. Especially extensions connecting to external sources, like Facebook, Twitter, Picasa, Flickr, etc can seriously extend the load-time of a page, because the external connection takes additional time.
However, really every additional extension will always take up some time. Well programmed extensions will take a minimal amount of time, so it also pays to check good sources for your extensions. Of course in most sites you will have to use some extensions, you can hardly build a ticket-selling website without an event manager, but whether you need a Twitter feed on all your pages is worth considering. Maybe you just need it on your contact page, which will free up the homepage.
Avoid sliders and carroussels
Sliders and carroussels should be avoided as much as possible. Though webdesigners and the customer who ordered the website often find these very attractive, actual users that visit the website often ignore them, or even treat them as ads to be blocked (banner blindness). Usability test have proven that they are mostly very ineffective and that no more then 1% of users evers clicks on a link or feature in the slider. You might want to check www.shouldiuseacarousel.com.
On top of that, they usually require multiple images and javascripts files, plus either MooTools or Jquery.
Remove MooTools / Jquery
Many simple templates could run very well withou any javascript at all. In 2.5 at least MooTools is loaded by default. MooTools is necessary for front-end editing, but also many sites do not use front-end access. In this case, or if functionality is already provided with Jquery, MooTools is loaded for no reason at all. Since it is quite a heavy Javascript library, it adds to your website load.
In those cases, you could try to prevent MooTools from loading. Either do some smart programming with a template override, or use an extensions like the Mootools Enabler/Disabler Plugin. It even allows you to still load the library under certain circumstances.
In Joomla 3, Jquery is loaded. Especially for responsive sites, it may be necessary for the Bootstrap responsive menu. Keep in mind though whether you really need it.
Joomla template
Make sure you check your template if you need to optimize your website speed. Templates with a lot of stylesheets, javascript files, javascript libraries slow down your website speed if not programmed properly.
Social media share buttons
Many sites have buttons to allow sharing to Facebook, Twitter, Google+ etc. In mot cases, every separate button requires a little bit of Javascript to connect to the network and possibly retrieve information to be displayed on the button, or behaviour when hovering over it. It should not be too hard to avoid that.
If you look at the share buttons on my site, they only link to an external URL, including the necessary data in this URL, as you can see in this example for the Google+ share:
<a onclick="javascript:window.open(this.href,'', 'menubar=no,toolbar=no,resizable=yes,scrollbars=yes,height=600,width=600');return false;" href="https://plus.google.com/share?url=https://joomla-seo.net/Performance/limit-joomla-extensions">Google+</a>
So, all your content can be shared, and it requires no external connections and bandwidth / latency.