Google returns 27,000,000 hits on "robotics". It is a very broad field. Perhaps you could do some thinking about a narrower aspect of it an look for more focused answers.
Take a look at some of the kits that are available here.
I would suggest that you may want to choose an inexpensive and simple kit and build one to see what is involved. Then you can decide whether you want to take it up a notch and design your own robot based off the kit or if you are comfortable with it you can start from scratch and design your own.
While not all robots are microcontroller based, You will find that the more sophisticated the robot the more likely it is to be microcontroller based.
A couple of popular microcontrollers are the PIC and AVR. You may want to do some investigating to see which one you want to learn.