To add a remote address book you have to choose the second option :
Then, you get this choice :
The first entry will create a CARDDAV address book, you will need to fill the URL to your remote address books, the user and the password. CardBook supports the DIGEST and BASIC authentication. CardBook supports the auto discovery on your server, which means that if your server also supports it, you might enter only the root url (example : https://yourserver.com).
The second entry will create a GOOGLE address book, you will need to fill only your email address.
The third entry will create a APPLE address book, you will need to fill your email address and password to your iCloud account. Be careful as Apple requires that you use application passwords (searching on the web will quickly helps you on generatign these passwords).
The fourth entry will create a YAHOO address book, you will need to fill only your email address.
Then, you need to click on the Validate button :
If you have chosen GOOGLE or YAHOO, you will be asked for allowing CardBook to access your contacts. Agreeing will result in a token that you don't have to copy, CardBook will store it in the Thunderbird password manager for next synchronisations.
If you have chosen CARDDAV or APPLE, due to some obscure core bugs, you might have to click three times on the validate button to have it validated. Generally, one click is enough. If your validation failed, it's time to look at the CardBook log, for inspecting the server answers.
Once the validation succeeded, the Next button is available, click on it :
In case you have multiples address books, choose which ones you want to add into CardBook, then choose their names, colors and vCard versions. Be careful that servers often do not support the 4.0 version, so prefer the 3.0 version. Uncheck the option Use Urn:uuid (unless you want to use long uid). The Work offline option allows you to cache your contacts into your Thunderbird profile (into an IndexedDB database) for an offline use. This option should be used for very large address books, which cache size might be an issue. CardBook will ask you for a subset of contacts that you want to work with. If you use a common size address book, let this option checked.