The process is very simple. Before you start, just make sure you have the Secret Recovery Phrase that is associated with your ID safely stored and accessible.
Then, follow these steps:
1 - Open Blockstack and click on "Settings":
2 - The following page will open. Select "Reset Browser":
3 - Confirm:
4 - Select "Sign in with an existing ID" and then enter your Secret Recovery Key or Magic Recovery Code:
5 - Create a new password, and store it safely (having a password manager can be very helpful).
6 - And finally - add the new e-mail and click "Next"!