As far as the phone development is concerned I would take a look at hackaday's tutorials on android development.
When it comes to the actual robot, you will need all your standard robot parts (batteries, mcu, motors, etc) in addition to a bluetooth serial device (they can be pretty pricey) but that's about it. Most of this project will revolve around programming the phone as the robot just has to be set up like it would for any remote control, ex. [this signal recieved go forward] [that signal recieved go backwards] [wait for new signal] [repeat]