In general, you can't.
Apple hase changed their most current releases of their iPhone development tools so that the minimum Deployment Target is iOS 4.3. Thus, any apps built with the current version of Xcode will not run on devices running older OS versions. Any developer who wants their apps to look good, or use the latest features on the latest devices (iPhone 5, etc.), can no longer submit apps or updates compatible with iOS 3.x. So a vast percentage of apps updated since Sept. 2012 are no longer compatible with an iPhone 3G, since a 3G can not be upgraded to iOS 4.3.
The iTunes App store only offers downloads of the latest version of an app from the App store, so older versions are no longer available (except to customers who have previously downloaded these old versions and made backups in case iTunes tries to trash these working versions.)
A few developers still use older development tools; and some apps have not been updated recently. Those fewer apps are the apps suitable for you device. But they may or may not be the ones you want.