Your question will require a very long answer
But first,
Does your board have external memory?
If it has one, learn first how to interface with it and store data there and read it back.
If it does not have, check what the available memory size of the FPGA chip is.
After that, how big is your source image size? is is small enough to be stored in the internal memory of the FPGA in case you don't have an external memory?
Your board should any way of communication to the PC. Assuming that the image is stored on the PC, learn how to interface the board with the PC and send/receive data.
In case your board has sdcard, learn how to interface with the sdcard to load the image or store the compressed one there.
Assuming that you did all of this and could successfully compress the image, you want to display the output. You should know that you cannot display a "compressded" picture. You will have to decompress it first. After that, if your board has a VGA interface, learn how to use that interface. This interface will need its image buffer to store the image that will be displayed on the screen.