To use vBulletin connection extension you can take next steps:

Notice: I assume there are two languages on site and forum

And the entire forum is divided on two sections: English forums and YourLanguage forums

1. Install newloginbox extension. Create SysFolder to store FE-users records. Create FE-user groups (at least one, e.g. “Registered”)

2. Install and configure vBulletin (last version 3.5.4) (e.g. in folder named forums). All actions are described in vBulletin manual. There is the only restriction – to locate vBulletin tables you must use your Typo3 site database.

3. Install and configure vBulletin connection extension. All settings seem clear.

4. Create a page (e.g. Login/Status) and place newloginbox plugin on it.

5. Just after the plugin place a text content element  with access “Hide at login” :

Forgotten your password? (link to forums/login.php?do=lostpw&langid=1)

Register (link to forums/register.php?langid=1)

Below add text having access: "Registered" :

Edit profile (link to forums/profile.php?do=editprofile&langid=1)

6. Make translation of the page to YourLanguage. Place on it a newloginbox and text content elements:

[Translated]Forgotten your password? (link to forums/login.php?do=lostpw&langid=2)

[Translated]Register (link to forums/register.php?langid=2)and[Translated]Edit profile (link to forums/profile.php?do=editprofile&langid=2)

7. To make link to English forums create a page (e.g. Forum) having type “External URL” and access "Registered" (link to forums/forumdisplay.php?f=1&langid=1). To hide the page in case YourLanguage is selected set checkbox “Hide page if no translation for current language exists”.

8. To make link to YourLanguage forums create a similar page (and of course its translation) with link to forums/forumdisplay.php?f=4&langid=2. To hide the page in case English is selected set checkbox “Hide default translation of page”.

Of course you must insert instead of f=1(f=4) index of your own forums (founded in AdminCP)

9. If you also want use vBulletin mail form, you can similarly to above create pages Contact us (link to forums/sendmessage.php?langid=1) and [Translated]Contact us (link to forums/sendmessage.php?langid=2).