You can purchase the iOS 3.1 Software Update for iPod touch (1st generation) from the iTunes Store using the latest version of iTunes on a Mac or PC.
Own an iPod touch (2nd generation or 3rd generation)? Get the free iOS 4 Software Update for iPod touch.
If you are not sure which model iPod touch you have, read this article: Identifying iPod models.
After you purchase the iOS 3.1 Software Update for iPod touch, iTunes will begin downloading the software to install on your iPod touch. Note that the download make take longer on slower Internet connections (the download is approximately 250 MB). To learn more about the update process that installs the software on your iPod touch, review the following article:
If you purchase and download the update on one computer but choose not to update your iPod touch on that computer, you can use a different computer to download the software. Simply attempt to purchase the update again as described above using the same iTunes Store account and you will be offered the option to download the update again free of charge.
Note: iPod touch (1st generation) is not compatible with iOS 4 software.