The display will either have a 14 or 16 pin connector.

Pins 1 to 14 are always the same wether they are all in a line or as two rows.

Pins 15 and 16 are the LCD back light if fitted (may be led type or EL type which will need an inverter).

Pin 3 is the contrast control pin.
This needs to be a voltage between 0 and 2 volts or -2 to 0 volts depending on type.
(BE VERY CAREFULL AS YOU COULD BREAK THE DISPLAY OR SYSTEM IT IS CONNECTED TO)

It really isnt something you can advise 100% over the net !!!

Get the data sheet for the new display and if possible the old one too. !!!