The fighters are loaded at a properly equipped facility like a star port. To load all the fighters the launch racks are withdrawn all the way to the back. A ring of fighters is then loaded on and the launch racks are forwaded by one fighters width. This process as suspected would take a very long time, though all effort was made to make sure as many fighters could be launched out as fast as possible. Plus with stasis suits none of the clones ever leave there fighters... unless they are shot down or captured.
The armored doors open and all the fighters fly out as fast as possible. Ideally the outer racks would launch first and then the launch cylinder would rotate 180 degrees and the inners racks would then launch. This way as many fighters could be launched out as possible with as little collisons as possible. However in a emergency launch situations, all fighters could launch though the inner racks would have to try and avoid each other during launch. In this situation close to 30% of fighters could be expected to collide. Launch times for all fighters usually are around the 20 second range.