If you don’t want to use a kit, how do you start making a robot? Where do you get the supplies?

Taking apart an old radio control car is a great place to start.  It has motors, a chassis and a battery already.  All you need to do is find a processor of some kind and make sure your control signals work.  While operating a radio-controlled car will not satisfy the requirements of the merit badge, taking an RC car, adding a controller (the computer brain that does the robot’s thinking) and some other mechanisms probably will.  As always, talk to your merit badge counselor first to make sure that what you are planning is safe and will satisfy the requirements.