If you backup to iCloud, you don't need a computer. To backup your iPhone in iCloud, go to Settings - your information - iCloud - iCloud Backup, and select Backup Now.
To backup to iTunes, you need a computer. You connect your iPhone to the computer using the cable that's also used for charging, open iTunes, wait for the iPhone to appear in iTunes and select it, then choose the Summary tab, and scroll down to Backups, where you click "Back Up Now".
To erase your device, go to Settings. In iCloud, disable "Find my iPhone". Then go to General - Reset, and select "Erase all Content and Settings". This will remove every informtion from your iDevice, and set it back to factory settings.
Hope that helps.