How to upgrade my iphone 3G from version 4.2.1?

When I go to download a newer app it says its not compatible with my iphone. When I try to upgrade my phone it says that Version 4.2.1 is the current version. And some others told me to restore my phone what does that do? And yes I'm sure my phone is only the iPhone 3G. What can/should I do
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Added (1). When I hit check for update is says its up to date and won't let me do anything.

3rd Generation should be able to update to the newest firmware 5.1.1. Plug your phone into your computer. When it loads in iTunes, press Update and give it a little bit of time.

If your phone is 3g that's the highest firmware you can get, Steven only 3gs can be updated to 5.1.1 not 3g