I present a study on calibrating the masses of galaxy clusters, the largest collapsed structures in the Universe, using the Sunyaev-Zel'dovich (SZ) effect. The SZ effect is a spectral distortion of the cosmic microwave background caused by the hot, ionised intra-cluster medium (ICM). Measuring the ICM in X-rays and the SZ effect, and calibrating those measurements to a reliable estimate of the cluster mass, is crucial for the use of galaxy clusters as cosmological probes. For my work, I obtained the integrated SZ effect (Comptonization parameter) from our observations with the APEX telescope for a sample of 27 X-ray selected galaxy clusters. The direct mass estimates of these clusters were obtained from our own weak-lensing observations. For modeling the mass-dependence of observables, I apply a novel Bayesian method to account for sample selection biases, measurement uncertainties, the shape of the cluster mass function, and scatter in the true mass-observable scaling relations. Importantly, I allow for a possible covariance between the X-ray luminosity and the SZ effect at fixed mass, which had been neglected in similar analyses in the past. I find that neglecting this covariance biases the normalization of the Comptonization-mass relation high and the slope low, even though the SZ effect did not play a role in the sample selection. I conclude that taking into account such covariances between the ICM observables is essential for the currently ongoing and next generation cluster cosmology studies.