You people might be aware for Apple Game Center launch, but apparently it was not for iPhone 3G. But if you are eager to do so first you have to jailbreak your iPhone 3G with redsnow 0.9.6b1, which allows you to jailbreak iOS 4.1 and iOS 4.0 on iPhone 3G and iPod Touch 2G. Below are couple of simple steps in order to jailbreak your device, follow them up :

How to Jailbreak iPhone 3G/iPod Touch 2G on iOS 4.1 :

Step 1: First you must download and install iTunes 10 from the link.

Step 2: Download iOS 4.1 for iPhone 3G from here, and for iPod Touch 2G from here.

Step 3: Next, download redsnow 0.9.6b1, or use the direct link.

Step 4: Install Redsnow and execute it.

Step 5: Select your stock or the firmware iOS 4.1 or iOS 4.0 ipsw.

Step 6: Proceed Next and then select ‘Install Cydia’ and proceed further with Next.

Step 7: Set your iPhone in DFU Mode. Now Hold the ‘Power’ button’ and simultaneously hold on the ‘Home’ button for at least 10sec. After 10sec, only release the Power button but keep holding the Home button until the update begins.

You are done, finally your iPhone 3G / iPod Touch 2G is now jailbroken instantly by redsnow.

Note : Follow this method on your own risk.