Your "thunderbird" program is an e-mail client.
Your e-mail address will be based on your domain, not dreamhost.com - for example if your domain was example.com then your e-mail address will be email@example.com
You should use your e-mail address when an e-mail client asks for your username.
The password is your mailbox password. While you can certainly use the same password if you want, the mailbox account and the web panel account are separate and so the passwords may be different.
If you forgot the mailbox password, in the Web Panel browse to "Mail -> Manage Mail" and find your mailbox. Click on "Edit" to change the password - it will take some time for the change to take effect, perhaps 15 minutes.
When the e-mail client asks for the incoming (IMAP/POP3) and outgoing (SMTP) server names, you should use a mail.* hostname. For example for the domain example.com the server name to give would be mail.example.com
However if you want a secure e-mail connection use *.mail.dreamhost.com - replace * with the name of your e-mail server (click on Account Status in the Web Panel)
The Thunderbird account wizard summary might look like this:
Account Name: John Doe
Email Address: firstname.lastname@example.org
Incoming User Name: email@example.com
Incoming Server Name: mail.example.com
Incoming Server Type: IMAP
Outgoing User Name: firstname.lastname@example.org
Outgoing Server Name (SMTP): mail.example.com