First of all; take a backup copy of your current installation, including the database!
Shut down your Tomcat server
Again, make sure that you have done a backup of your Tomcat webapp (all files) and the database!
Extract the content from 'vp_installed_v6.2_upgrade_from_v6.1-20100602.zip' over your current installation.
Update your VisionFlow database by running the SQL script 'upgrade_from_v6.1_to_v6.2.sql' located in the directory: '/WEB-INF/internal_docs/installed version/db_scripts/v6.2/Upgrade from v6.1'. Choose the directory that match your database, MS SQL Server or MySQL.
You are done and can start Tomcat again!