How to upgrade from iOS 4 to iOS 6 without losing app data
Make a backup and then restore the backup once the update has finished. 

A step by step guide is available here: http://support.apple.com/kb/HT4972, which states the following:

To update your iPhone, iPad, or iPod touch from iOS 4 to iOS 5 or later, you must erase and restore your device first, before completing the update.

As part of the update and restore process, iTunes will (in order):


Back up key elements of your device, such as settings, Contacts,
Calendars, Notes, and your Camera Roll. iTunes will not, however,
back up media content from your iOS device, such as music, apps,
books, movies, and TV shows.
Update your device to the latest version of iOS software.
Restore your device from your most recent backup.
Restart your device.
Sync back media content from your iTunes Library to your device.