Q: How do I close non-Internet apps on iPhone?

Tapping the Home Button closes any App, but they are placed in the multitasking tray for quick access should you re-open them later. If you want to fully close an App, double-click the Home button, and then remove the Apps from that tray the same way you would delete an App.

You're co-worker is incorrect. Very few apps actually run in the background. The notable excecptions would be navigation apps and apps that play music. If you need to shut down an app that's misbehaving, double tap the Home button, than press and hold one of the icons until they start to wiggle. Tap the minus sign.

Don't stress about quitting apps as a general practice. It's a waste of your time and accomplishes nothing.

There's no need to close apps, but if you really, really want to for some odd reason see the manual, page 19.

http://whenwillapple.com/blog/2010/04/19/iphone-os-4-multitasking-explained-agai n/

http://support.apple.com/kb/HT4211?viewlocale=en_US&locale=en_US