The connections that worked were as follows (1602 connections first):-
pad 1 = VSS and connects to GND on UNO.
pad 2 = VDD and connects to 5V on UNO.
pad 3 = V0 (display contrast) and connects to GND on UNO. ** see note below
pad 4 = RS and connects to D12 on UNO.
pad 5 = R/W and connects to GND on UNO.
pad 6 = Enable and connects to D11 on UNO.
pads 7, 8, 9 and 10 are not connected.
pad 11 = D4 and connects to D5 on UNO.
pad 12 = D5 and connects to D4 on UNO.
pad 13 = D6 and connects to D3 on UNO.
pad 14 = D7 and connects to D2 on UNO.
pad 15 = A (anode) and connects via a 270ohm resistor to 5V on UNO.pad 16 = K (cathode) and connects to GND on UNO.
** The connections on the arduino.cc page show this connected to the wiper of a 10K pot (pot connected to 5V and GND). However I found that the display contrast was right with the pot turned to zero, so to simplify things I've removed it and simply connected pad 3 to GND. If the contrast is too strong you may need to add the pot.
Test sketch / program is below, you should be able to cut and paste this into the Arduino IDE.
The only LCD library required is "LiquidCrystal" which comes pre-installed with the Arduino IDE (at least on version 1.0.1 and 1.0.5 that I've checked). So hopefully compiling the program will not be a problem.