Raspberry PI GPIO uses 100 mil spacing dual row header like in the picture below:
At the moment it is unclear what kind of connector is there on your e-ink display. Assuming that you have a similar kind of connector, you can use DuPont cables to wire up your display. DuPont cables are pretty cheap and abundant on eBay. A picture of DuPont wires is below:
Here is the GPIO pinout of Raspberry Pi:
According to the pinout, you have to use the following SPI pins:
GPIO10 - SPI0_MOSI
GPIO9 - SPI0 MISO
GPIO11 - SPI0 SCLK
GPIO8 - SPI CE0 N (optional if only one device on bus)
Please do elaborate your question so that this answer can be more precise to your question.
EDIT:
From your addition it looks like that your display uses FPC cable. One option you have is to manually solder SPI wires to the FPC cable if you possess soldering finesse. Otherwise, you would have to design a PCB that incorporates a FPC connector and header pins. Check with the manufacturer if they offer any conversion options (see below picture):