There are loads of things that can be done.
Update to Joomla 3.5
I've have just done this on all my sites and the back-end especially is so much faster at executing database queries.
If you can update your server's PHP version to 7, then do so. The performance increase is very big. But make sure your extensions are PHP7 compatible.
Look into caching your CSS/JS files and images. I'd recommend using JCH Optimize. When going through the setting available, don't simply switch everything to the max as you'll run into issues. Try each one individually, each time checking your browser console to see if any errors occur.
Use a 3rd party Speed Test tool. I personally recommend Pingdom Tools. After running a test, it will tell you what you're currently doing wrong on your site and how to fix/improve it. Another site you can also use is GTMetrix
Hope this helps