1. First, log into your concrete5 site as an administrator
2. Log into your server's control panel and backup the database (or the entire site if you wish)
3. Download a new zip of concrete5, extract it, rename the concrete folder inside it to something like concrete_new, zip that up and upload it next to the existing concrete directory
4. Unzip the uploaded zip of the new concrete_new directory
5. Rename the existing concrete folder to something like concrete_old, and the concrete_new to just concrete (you're swapping them over)
6. Immediately visit /index.php/ccm/system/upgrade and perform the upgrade

After upgrading you can then delete the concrete_old folder and concrete_new.zip file from your server as they are no longer needed.

it is often suggested that you turn of caching of your site, clear the cache and then turn it back on after the upgrade is performed.