i have apple iphone 3G, how can i update software to download games

If it is a iPhone 3G then you can't, it only supports up to iOS 4.2.1

If it's a 3GS then yes, it can be updated to iOS 6.1.6 (you can only update a device to the highest version that it supports, so you can only update to 6.1.6, you can't update it to, for example, iOS 5) - you can oly update it by connecting it to computer's iTunes.

To update it, connect the phone to your computer's iTunes and copy any purchases off the phone to your computer via File > Devices > Transfer Purchases. You may also want to copy photosand any important documents off the phone as well e.g. via the file sharingsection at the bottom of the device's apps tab when connected to iTunes, via wifi, email, dropbox etc - they should be included in the backup, but it's best to havea copy of them outside of the backup just in case. You can then force a backup of the phone via File > Devices > Back Up.

Then start the update by selecting the phone on the left-hand sidebar (you can enable the sidebar via option-command-S on a Mac, control-S on a PC), and on the Summary tab on the right-hand side clicking the Check For Updates button

Updating to iOS 5+ : http://support.apple.com/kb/HT497