This video will show you how to install Skype on iPhone 3G 4.2.1. Your iDevice needs to be Jailbroken before you attempt this video. See the links below for help on that.
NOTE: Skype no longer supports iOS 4.
https://support.skype.com/en/faq/FA34493/is-skype-for-ios-being-discontinued-on-ios-4-and-below 

How to Backup
How to backup your iPhone click here.
How to Restore
How to Restore your iPhone click here.
How to Jailbreak
How to Jailbreak your iPhone here.
Where can I download the Skype App?
You can download the Skype App and other Apps under the Apps section of this website. However the direct link for the Skype App is here.