For The Financial Edge: 
How to add a new bank account
How to globally change the Bank account on a vendor record

How to globally change bank account on posted or unposted invoices
Please see Banks Guide for complete information. 

For The Raiser's Edge: 
How to add new bank information 

Additional Note: If you post from The Raiser's Edge into Financial Edge and want gifts to post to this new bank account you will need to go into the funds in Raiser's Edge, click on the GL Distribution tab and change the account number there to the new GL Account number from the new bank account or use the following solution

Blackbaud Merchant Services
To create a new account please see How to set up a Blackbaud Merchant Services Account
To change the bank on an existing account please see How to edit a bank account in Blackbaud Merchant Services (BBMS)

Blackbaud Net Community

If your organization uses BBMS, please see steps above.
If you want to add a disbursement account to have funds deposited into multiple accounts, refer to How to Distribute Funds to multiple Disbursement Accounts.
If your organization uses a third party merchant provider, contact the merchant to update the banking information.