I recently installed this driver on Ubuntu 15.10 64bit.
First download the driver from Canon's website. The URL has changed from previous answers.
https://www.usa.canon.com/internet/portal/us/home/support/details/printers/black-and-white-laser/mf4770n
The Canon website may autodetect your browser as generic Linux instead of 32bit or 64bit. If this is the case, select the correct one to see the specific driver to download. Extract this file (.tar.gz) through the file browser or terminal. Next, enter the directory and install the driver (your driver version may be newer).
cd ~/Downloads/Linux_UFRII_PrinterDriver_V310_us_EN/
sudo sh install.sh
After this is complete, you can go into your System Settings -> Printers and add it as a network printer. For me, the driver was autodetected and I only needed to name the printer.