Connect the iPad to your computer's iTunes and copy any purchases off the iPad to your computer via File > Transfer Purchases (File > Devices > Transfer Purchases on iTunes 11). You may also want to copy photos and any important documents off the iPad as well e.g. via the file sharing section 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 have a copy of them outside of the backup just in case. You can then force a backup of the iPad by right-clicking the iPad 'Device' on the left-hand side of iTunes and selecting 'Backup'.
Then start the update by selecting the iPad on the left-hand sidebar of iTunes (on iTunes 11 you can enable the left-hand 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/HT4972
Your iPad should be updated to iOS 6.1
You need iTunes, not the Apple Store, in order to update your iPad.
Connect the iPad to your computer with the cable.
Launch iTunes - if it does not start up on its own.
Click on your iPad's name under the device heading in the left sidebar of iTunes.
Click on the Summary Tab in the iTunes window on the right - at the top of the window.
Click on the Check for Update button.
If you are running iTunes 11 - and you can't see the sidebar - at the top of the screen go to View>Show Sidebar.
If you need iTunes, you can download the latest version here.