In July of 2012, both the ATLAS and CMS experiments announced the discovery of a new particle consistent with the Standard Model (SM) Higgs boson. This has ushered in a new era of precision physics: measuring the Higgs boson's properties. Precisely measuring all the properties of the newly discovered Higgs boson will tell us if this is the particle predicted by the SM or another particle entirely. This thesis focuses on cross section measurements of the Higgs boson in the diphoton decay channel. The analysis is preformed using 4.5 fb-1 and 20.3 fb-1 of proton-proton collision data recorded by the ATLAS detector at CERN's Large Hadron Collider in 2011 and 2012, at centre-of-mass energies of 7 TeV and 8 TeV, respectively. Fiducial cross sections are measured and corrected for experimental effects such as detector acceptance and resolution. The results are compared to the latest state-of-the-art theoretical prediction for SM Higgs boson cross sections.The Higgs boson signal is extracted and the background subtracted by performing a signal plus background fit to the invariant diphoton mass spectrum. The pp -> H -> gamma gamma inclusive fiducial cross section is measured to be 45.3 +/- 16.9 (stat.) +5.3 -5.3 (syst.) +/- 0.8 (lumi.) fb at 7 TeV and 43.2 +/- 9.4 (stat.) +3.2 -2.9 (syst.) +/- 1.2 (lumi.) fb at 8 TeV, for a Higgs boson of mass 125.36 GeV. Using the larger 8 TeV dataset, additional fiducial and differential cross section measurements of the Higgs boson are also reported. This thesis will particularly focus on the following aspects of the Higgs boson cross section measurements: (i) jet calibration and performance, (ii) a data-driven method for obtaining the diphoton background rate estimations required for deriving the background parameterization used in the signal extraction, (iii) extracting the Higgs boson signal by performing a simultaneous s+b likelihood fit to the diphoton invariant mass spectrum, and (iv) deriving the `unfolding' factors used to translate the measurements to a set of detector corrected model-independent observables.