Begin by looking at the datasheet for the 74HC595 here http://www.nxp.com/documents/data_sheet/74HC_HCT595.pdf. Look closely at the board to see which pins are connected to the connector for you to use.
These displays usually have several of these serial-input shift registers connected so you can load in a row of data, (multiples of 8 bits at a time), and light just one row of LEDs with that data. Then you need to load the next row and light it. By lighting each row in sequence, too quickly for the eye to see the flicker, you can give the illusion of having all the LEDs for a piece of text lit at once, even though they are really lit one row at a time.