We report a comprehensive experimental investigation on the magnetic anisotropy in bulk single crystals of Cr2Ge2Te6, a quasi-two-dimensional ferromagnet belonging to the family of magnetic layered transition metal trichalcogenides that have recently attracted a great deal of interest with regard to the fundamental and applied aspects of two-dimensional magnetism. For this purpose electron spin resonance (ESR) and ferromagnetic resonance (FMR) measurements have been carried out over a wide frequency and temperature range. A gradual change in the angular dependence of the ESR linewidth at temperatures above the ferromagnetic transition temperature Tc reveals the development of two-dimensional spin correlations in the vicinity of Tc thereby proving the intrinsically low-dimensional character of spin dynamics in Cr2Ge2Te6. Angular and frequency dependent measurements in the ferromagnetic phase clearly show an easy-axis-type anisotropy of this compound. Furthermore, these experiments are compared with simulations based on a phenomenological approach, which takes into account results of static magnetization measurements as well as high temperature g factors obtained from ESR spectroscopy in the paramagnetic phase. As a result the determined magnetocrystalline anisotropy energy density (MAE) KU is (0.48±0.02)×106 erg/cm3. This analysis is complemented by density functional calculations which yield the experimental MAE value for a particular value of the electronic correlation strength U. The analysis of the electronic structure reveals that the low-lying conduction band carries almost completely spin-polarized, quasihomogeneous, two-dimensional states.