Have to make a program that given the option to input square or circle, user inputs width and a center x,y coordinate. 
What I don't understand is how to write code for if there are two shapes on a plane and how to identify if one is inside the other
I'm super helpless, and have no background in computer science. Thank you!
You have to address Circle in Circle, Circle in Square, Square in Circle, and Square in Square.  I suggest drawing some pictures with the centers marked, and observe their relationships.
Circle in Circle: the distance between the centers has to be less than the difference in radius's.   
Circle in Square: Same as circle in circle I think
Square in Circle: The radius of the circle must be larger than the distance from the center of the square to a corner PLUS the distance between centers
Square in Square: you got this! solve yourself ;)
Python Shapes on grid