Once you have D-Dog unlocked, just start bringing him along on every mission and petting him with
every once in awhile and eventually, your bond will go to the max. He'll point out enemies, wild animals and medicinal plants for you, and proves to be very useful. As well, while he can be spotted by enemies, doing so won't give your position away, as they'll just shoo him away.
Once at max, you'll be able to customize him by changing his colour or changing his hurt eye by taking the eyepatch away or giving him a prosthetic eye.