To upgrade an existing version of iZeit, first upload the new files to your server, overwriting existing files. To start the upgrade, go to http://yourdomain/path/to/izeit/index.php?act=upgrade.
If you want to save your current events and tasks, you'll need to create a backup from the control panel first. When you've done this, start the upgrade by clicking 'Next'. The backup can be restore when the upgrade is complete, but is likely to need updating in order to be compatible with the latest version. Send the backup file to firstname.lastname@example.org, and you should get an updated version within a day.