If you just want something that ‘works’ for a video game, refer to 2 Joint 2 Limb Inverse Kinematics
If you wish to build a strong mathematical background and understanding regarding Inverse Kinematics, it will require more work. CS223A at Stanford, which is ‘Introduction to Robotics’ requires Linear Algebra and Calculus as a prerequisite. If you have not taken those courses, I would recommend you do so (or self study). You should then be able to parse coursework regarding basic kinematics and motion. Refer to http://www.cs.cmu.edu/~15464-s13/lectures/lecture6/IK.pdf for a holistic overview on basic kinematic modelling and methods for Jacobian inversion.