I am new to the world of Arduino. I'm making the project a spider robot, but my teacher does not help me and not where to start!
How do I program the movement of the legs? 
Could control the robot from a mobilphone?
Can I make my own wireless controller? XD
Thank you. Andrew 
The programming tou will have to figure out on your own unlesa you provide some info about the hardware,
Id suggest a bluetooth serial module and a phone that has a bluetpoth serial app for mobile phone communications
The nrf24l01 is a good cheap wireless transciecer and with an arduino nano can make a nice controller
And anything is possible lol
Are you new to the world of electronics? How about robotics? Have you built anything remotely this complicated in the past?
Depending on your answers to the above questions - this may be a project way out of line with your skill level (something else to keep in mind: such a robot project may also not be inexpensive - depending on the materials you use; at a minimum expect to spend more than $100.00 USD - possibly a LOT MORE).