Randomizing pixel location

For a class I need to create a simple computer game. Here is the general idea of that game.
When the up button is pressed, the invader will start moving and a dot will appear on the screen. Use the joystick to move the invader so that it hits the dot. If it hits the dot, the dot disappears and another one appears somewhere else on the screen. Hit as many dots as you can. The game ends either when 28 seconds are up, or when the invader hits the boundary rectangle. The score is the number of dots hit. After 7 seconds, 1 obstacle appears on the screen. After 14 seconds, another obstacle appears on the screen. After 21 seconds a third obstacle appears on the screen. (obstacles will be rectangles that appear on the screen at the given increments).

I haven't had much prior experience with C and and am struggling with programming the dot to randomly appear, disappear when it gets hit, and then randomly appear somewhere else. If anyone could help me with how to program that it would be greatly appreciated.

This cannot be done purely in standard C, so it would be helpful to know what relevant libraries your teacher has taught or recommended that you use for this exercise.