We use angle-resolved photoemission spectroscopy to investigate the electronic properties of the newly discovered iron-arsenic superconductor Ba_(1-x)K_(x)Fe_(2)As_(2) and nonsuperconducting BaFe_(2)As_(2). Our study indicates that the Fermi surface of the undoped, parent compound BaFe_(2)As_(2) consists of hole pocket(s) at Gamma (0,0) and larger electron pocket(s) at X (1,0), in general agreement with full-potential linearized plane wave calculations. Upon doping with potassium, the hole pocket expands and the electron pocket becomes smaller with its bottom approaching the chemical potential. Such an evolution of the Fermi surface is consistent with hole doping within a rigid-band shift model. Our results also indicate that the full-potential linearized plane wave calculation is a reasonable approach for modeling the electronic properties of both undoped and K-doped iron arsenites.