How to upgrade my iPhone 4.2.1 to iOS 5 or 6?

It's the iPhone 3, but on the home screen it looks like the First iPod touch generation and I wanna update it so I get instagram and Facebook and twitter. And so I can put a wallpaper on my home screen Should I take it to apple?

You can't, apple stopped supporting the iPhone 3-3GS on updates, and anything below it.
Same goes for the iPods 3rd gen and before

Plug it in to your computer while iTunes is open. Apple will pop up a message that will ask you if you want to update it. Click update. Once you do, re-sync the iPhone, and music, photos, etc. From your computer will be transferred to your iPhone.
Hope this helps,
ET

On the home menu, you should see the "Settings" icon, which looks like a set of cogs. After you open that, go to the 6th item on the list which says "General". Second item on that list is "Software Update", which you need to click. After that, the iPhone should tell you that you need an update and ask if you want to update it then and there. You want to be on Wi-fi when you do this just to make sure you can download the whole thing in a timely manner. So to summarize:
Home > Settings > General > System Update

Iphone 3 is not supported. The lowest iphone supported is the 3GS. Even if you had the 3GS you won't have few of the ios6 features.

http://ipod.about.com/od/iPhoneQandA/f/What-Devices-Are-Ios-6-Compatible.htm

Not sure if it's the same on the iphone but on my iPad I would go to settings and the update to check for updates.