In the summer of 2023 multiple Pulsar Timing Array (PTA) projects have released their latest datasets and published the results of their searches for nanoHertz gravitational waves (GWs) in those data. The results are considered to be the first evidence for a stochastic background of GWs (GWB). By now, those results have been cited > 1000 times on the arXiv, and many research groups have used the results to do astrophysics and cosmology. In this presentation I will introduce and discuss the basic data analysis methods, and I will describe what parts of the analysis are reliable and which parts of the analysis should be improved. Many of the improvements I discuss have not yet been applied to released datasets in published work.