An access to D-Walker will be unlocked after quite a long time however it does not require you to do anything special. All you need to do is to complete the 13th main mission of the Metal Gear Solid V which is called Pitch Dark and is the first mission from Africa.
Information about D-Walker and how to use its help
D-Walker is not the most useful buddy since he has very limited variety of actions. He is an alternative way of transportation (kind of like a D-Horse) and is a very strong source of damage. At the beginning this machine is fairly week since it has just a weak handgun so you shouldn't even consider taking it with you if you haven't invented in an additional rocket launcher or a Gatling gun. Remember that most missions may be completed without even being detected so taking D-Walker with you should be an option only if you are sure that you will be forced to fight with a lot of enemies, like during the battle with the Skulls or the battle with tanks.