1. Update Joomla
2. Clean Up Joomla
Remove unwanted / unused components, modules , plugins.
Check for leftover database tables of old components or plugins and drop those tables.
Optimize and repair the database tables. Use PhpMyAdmin for this.
3. Optimize and resize your images
You could use a plugin such as WP Smushit which automatically reduces image file sizes every time you add an image to a page or post. Recommend that you use a GIF or JPG file
4. Use Caching
5. JCH Optimize
This plugin combines your external JavaScript and CSS files into one to minimize expensive http requests.
http://www.buildajoomlawebsite.com/blog/extensions/speed-up-your-joomla-website-with-jch-optimize
6. Use CDN (Content Delivery Network)
A CDN is a way of placing copies of the data from your website on several fast secure servers which respond to requests from the server nearest to the user. This increases the loading speed of your website and can be used in conjunction with a caching plugin.
Free CDN : CloudFlare