The ISS modules were launched pressurized, if for no other reason than that to pressurize them in orbit would be a drain on ISS resources.
The mechanical interface between a new module and the ISS is the Common Berthing Mechanism (CBM), which has been discussed on this site quite a bit. This answer will focus on the process of opening a pressurized path from the ISS to the new module.
The CBM forms a ring around the hatch, shown here.
Of interest to this answer is the Manual Pressure Equalization Valve towards the bottom of the hatch.
Our working example will be the Japanese Experiment Module (JEM), carried up on STS-124. I couldn't find a photo of the CBM end of the module so here is a graphics rendering of it. The red A labels the hatch/CBM on the JEM and the red B labels the hatch/CBM on the ISS where the module will be attached.
Once the robotics/CBM magic happens and the JEM is mechanically installed, a "vestibule" has been created. I couldn't find a good schematic of this so I drew up a terrible one. This tries to show a view looking perpendicular to the long axis of the JEM
This vestibule is formed by the rings of the CBM and the hatches on either side. Once the module mating is complete, the vestibule is at vacuum and the ISS and new module are at normal pressure.
NASA has chosen to not publish any Assembly Ops Checklists on the web but spaceref did, for the US Lab. The procedure is called VESTIBULE PRESSURIZATION AND LEAK CHECK and starts on document page 121. In brief, it describes how, on the ISS side, a crewperson will open the MPEV and allow air to flow into the vestibule from the ISS. Once a period of time has elapsed, or the flow stops, the MPEV is then closed, and time is allowed to elapse to ensure that the vestibule does not have a leak.
Once everyone is happy that there is not a leak, the MPEV is re-opened, and the ISS hatch is opened. The MPEV on the new module is then opened, and once equalization is complete, the module hatch is opened.
The module can now be accessed and outfitting can begin.
Here's an excerpt of the procedure: