Here's some info that should be of help:
http://www.national.com/an/AN/AN-440.pd
This app note basically describes exactly the command flow necessary to use this board. It uses an MM58341 and MM58348---these are the same as the two ICs you have, except they only ouput up to 35V (your two can go as high as 60V).
What these two ICs don't drive, however, is the filament of the VFD. This can be either an AC or DC voltage, the magnitude of which varies with the display. DC voltages are generally only supposed to be for small displays on like car audio systems, but I've used DC to filaments meant for AC. The only issues with this are that large DC voltages may potentially damage the display filament (or so Ive heard), but more noticeably, that the resistance of the filament causes a voltage drop along the length of the display that causes a distinct difference in brightness from one side to the other. Basically, you'll have to try and see. Check this for a little more info:
The hardest part of this will be writing characters to this. Each 5X7 character will needed to be stored in a look up table on the arduino (i'm sure there is some code written for graphic LCDs that you can reuse for this).
If you don't know anything about VFDs, they work like this: a voltage is applied to the filament sufficient to heat it to the necessary temperature. Another voltaqe is then simultaneously applied to one or more grid connections, and one or more anode connections (in this case, dot connections). Each dot and/or symbol (for displays that dont use dots) that share those one of the grids and one of the anodes driven lights up. Usually, it's most useful to "strobe" one of the two, so that you can control each dot/segment/symbol individually. I've never used a dot matrix VFD, so I assume that each grid covers a different digit, and the anodes correspond to the 35 pixels of each digit.
Basically, to get this to work, you need the right voltages, a software serial library to shift the data out with (NewSoftSerial seems to be recommended nowadays), and, most importantly, to read the first pdf I linked, since it describes exactly what you are doing.