Go to Plugins -> Add New and use the search function to browse and find the plugin you want form the WordPress.org plugin website.
In this case we want to install the plugin WP Super Cache to speed up the site response time.
After the search you will see an overview of plugins that showed up with the search string that was used.
For every plugin you will see the Name, Version, Rating and a short description. We are going to use the WP Super Cache plugin.
Now you have to click the Install now option to get it into your WordPress installation.
After successful installation you need to activate the plugin to get it working.
WP Super Cache needs some extra configuration so follow the instructions that show up after activation.
WP Super Cache Configuration
The first option is to go to the Wp Super Cache plugin admin page to enbale the caching option
Once you get to that page you will see a notification that your wp-config.php is updated or needs to be updated. Here you can set the Caching to On.
Now switch to the tab Advanced
Make all the options active that have the (Recommended) field behind them. Take special care for the first option, use .htaccess for cache rules.
You can set the cache time to what suits your site, for an active blog leave the default value. If you have a less active blog, set the time to 14400 seconds = 24 hours.
If you use the Mod_Rewrite option, check and update Mod_Rewrite Rules by clicking to button below the rules overview. Scroll down to see that screen. Once you click that button the screen will go to green if it worked correctly, otherwise you will have to update the .htaccess file yourself via FTP
Now you are all set and you should see an improvement in site loading time.
Other options are the W3 Total Cache Plugin or the Hyper Cache Plugin. The first one has a lot more options to set, the later is very easy to install and use, it only needs the cache function set in your wp-config.php.file.