How to backup your wallet and password - TheDAO/DAO-1.0 GitHub Wiki

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Using Mist - Backup Accounts

Go to the top bar and select ACCOUNTS -> BACKUP -> ACCOUNTS.

This will open a folder. Inside this folder there are keystore files that have long names starting with UTC--2016-04-14....... Each of these files represent an account. Backup these files.

Using Mist - Backup Wallet Contracts

Go to the top bar and go ACCOUNTS -> BACKUP -> APPLICATION DATA. This will open a folder. Just back up this entire folder.

You could also manually add the wallet contracts back at any time, obviously, but this is easier and more convenient.

Further advice on how to actually back up

You want to store the keystore files in multiple locations & multiple physical locations. Keep in mind, you must prevent loss of both the keystore file and password due to loss or failure of you hard drive, USB drive, or whatever method you are using to back up. You also must keep in mind physical loss / damage of an entire area (think fire or flood).

It is recommended to store backups in three places:

  1. On your computer.
  2. On a USB in your apartment but in a different room than your computer.
  3. On a USB at a different location.

You can additionally use a cold storage wallet - a paper wallet which is printed, but there is no paper option directly from Mist.

This way if my house burns down, I still have my accounts. If my HDD crashes, I still have my accounts.

If you want a paper option, you can import your Mist keystore file into MyEtherWallet (running offline/locally). Follow those instructions and use the View Wallet Info tab in order to access your Mist wallet and then print a paper version.

Source: ethereum.stackexchange.com, tayvano