In this talk, we start with the review of the ground state of steady state solutions of nonlinear Klein-Gordon equations defined on N dimensional space. We shall follow Beresticki and Lions (1983) to give a concise illustration of constrained minimization method to build up the existence theory for certain type of semilinear equations including nonlinear stationary Klein-Gordon equations. If time is allowed, further properties such as exponential decay of the solutions will also be demonstrated.