Just to be certain, we are talking about version 31.5.0 of Thunderbird. Correct? If not, then you have an old copy as of today and should upgrade it. These instructions are for the Windows implementation of Thunderbird. If you have a Macintosh, the configuration dialogs may be different. (Linux is mentioned after all of the Windows instructions but the same thing applies to Linux.)
The first dialog that comes up for adding a new account says "Mail Account Setup" in the title. There are four fields, "Your name", "Email address", "Password" and a "remember password checkbox". Check the checkbox and fill in ote htoer fields. Don't forget to include the domain name in the "email address" field. Click on the button marked "Continue".
The Next dialog says "Configuration found by trying common server names". It has a radio button for IMAP or POP3. Choose IMAP. It shows the incoming and outgoing mail information. Mine says "IMAP, mail.xxxxx, STARTTLS". We added a "smtp" to the DNS so it says that for the outgoing connection. If you didn't then it would still say "mail.xxxxx"
It will strip the domain name from the username field. This won't work, but there is a buttons marked "Get a new account", "Manual config", "Done", and "Cancel". Make sure that the connection is still IMAP and choose "Manual config".
The next screen shows items for the incoming and outgoing mail. Set the following:
Incoming: protocol=IMAP, server hostname=mail.xxxxx, Port=993, SSL=SSL/TLS, Authentication=Normal Password
Outgoing: protocol=SMTP, server hostname=smtp.xxxxx, Port=465, SSL=SSL/TLS, Authentication=Normal Password (Again, we put "smtp" into the DNS. Use "mail" if you don't.)
Username: xxxx@yourdomainname <<< DON'T FORGET TO CHANGE THIS. It will change both incoming and outgoing names if you just change the incoming field.
There are buttons for "Get a new account", "Advanced config", "Re-test", "Done", and "Cancel". Choose "Done". This will just create the account. Once the account is created, you can go into it and change the parameters for the connection. But, the "biggies" (server name, user name, password, port number, protocol) have been specified.
I checked with my copy of Ubuntu Linux 14.10. (Thunderbird is not just for Ubuntu so the platform is of little importance. RedHat and Ubuntu and Debian all use the same program, Thunderbird.)
The dialogs are slightly different in that the protocol is not specified on the first dialog but the second under the incoming section. Other than that, the buttons and the dialogs are the same. The input fields are the same.
I have not checked with the Macintosh laptop, but I typically use Apple's mail package and not thunderbird there.
Do not choose retest under any circumstances. This will only complicate your life as the retesting won't work and you will need to correct the fields but you will only have the option to re-test again. Just choose manual configuration and enter the values. Then click Done, not re-test.
In either case, you may get a warning that the certificate for the domain does not match the owner. You will be asked if you wish to accept this. Accept it and mark it "accept always". This only means that "mail.xxxxx" is using SSL and the certificate is not issued to you but DreamHost. You can buy your own certificate but it is probably not worth the expense to avoid the warning dialog. Just use Dreamhost's certificate and accept the override.