I have parity installed and running in computer1. Suppose I need to access my wallet from computer2, what should be done?
From the shared link in the other answer:
The Parity recovery phrase is a 12-word mnemonic phrase allowing you to have an additional backup. It's displayed once after account creation and should be written down or printed out and kept in a safe place. This phrase is not protected with any password or encryption and should always kept offline and cold. In the rare case that your encrypted backups (see below) are corrupted or lost, the phrase allows you to fully recover your private key.
Exporting accounts via the Wallet UI
The most convenient way to backup your accounts is via the wallet UI which offers direct export of the encrypted key files in JSON format.
A single account
To backup a single account, just open your accounts view, click the account you wish to export, and find the EXPORT button.
Once you enter your passphrase and confirm, the key will be exported and downloaded to your disk.
All accounts at once
To backup multiple accounts, or all accounts at once, just open your accounts view and find the EXPORT button.
Toggle which accounts you wish to export by clicking them, and thus enabling or disabling the account export.
Enter the password for each account you wish to export and confirm.
Restoring options work analogue to the backup options explained above.
The user interface allows you to import keys from:
- Geth Keystore: This allows importing keys created in with the go-ethereum client.
- JSON Backup: This allows importing password-encrypted JSON key-files previously exported with Parity.
- Private Keys: This allows importing plain, unencrypted private keys generated with any other application.
Presale Wallet: This allows importing a wallet from the initial Ether pre-sale maintained by the Ethereum Foundation.
In addition, it's possible to restore private keys from the 12-word mnemonic recovery phrase.
Please see this How-To that describes the process very nicely.
Let me know if you have further questions.