Tutorial: Backing Up A Private Key
Warning: There was a known error in the past versions of NEM and the following instructions did NOT work. From releases 0.6.42 on the back up wallet feature works.
You can always write down your private/public keys and address manually if you are using an old version, then update.
Your wallet is just a file on your computer. And since we know that every hard drive breaks (you just don't know when) a backup of your wallet is highly, highly recommended.
To do this click on the drop down arrow in the upper right hand part of the screen (next to your wallet name) and select “Export Wallet”.
You will now see a download with your wallet file in a zip compressed folder. Please save the zip file in a safe place (not your hard drive, but a USB drive e. g.).
Remember: Without your password the wallet is useless.
If you're keeping the USB drive in a box or something, it may be worthwhile to also write down the password to it in a separate location such as your wallet if you forget passwords often.