You found a pretty nice display, it includes the BCD and to 7 segment for you; that way you can control the segments with four lines, not including the multiplexing.
I can't hold your hand using this, I'll give some input though.
You have a simplified diagram of how the display works here in the datasheet:
So the main signal pins that you have to use are A through E with L to I.
Like Alex said, you need to activate each transistor (A to E) one at a time, to turn on a single digit. Activate A to show Digit 5, activate C to show digit 2.
L through I controls what number is displayed on the digit that is activated. So if you want '5' on digit 2, set C HIGH and write "0101" to JKLI respectively.
The datasheet is nice enough to provide a reference:
So the idea is to turn on one of the digits for a short period of time, and display the number you want on that digit. Then cycle through the rest and set the correct binary value for the respective digit.
If you want "1234" displayed: activate A and drive "0100", activate E and drive "0011", activate D and drive "0010", activate C and drive "0001". The idea is you cycle through the 4 digits so fast that a user cannot tell they are being blinked. Which is called multiplexing.
Ok, that's a lot more help than I was planning on giving but I needed a quick break from work. Good luck.