To perform the update, either follow the instructions from the Administration Control Panel->System Tab – this should point out that you are running an outdated version and will guide you through the update – or follow the instructions listed below.

Go to the downloads page and download the latest update package listed there, matching your current version.
Upload the archives contents to your phpBB installation – only the install folder is required. Upload the whole install folder, retaining the file structure.
After the install folder is present, phpBB3 will go offline automatically.
Point your browser to the install directory, for example http://www.example.com/phpBB3/install/
Choose the “Update” Tab and follow the instructions