So I have two layers that I am adding into ArcMap. I know for a fact that when you added the first layer with Projected Coordinated System, the 2nd layer, which has a geographic coordinate system will project on the fly. My question is what would happen if the Geogrpahic coordinate System is added first. What would happen and what are the necessary steps to have them all fit properly in the same coordinate system ?
ArcMap adopts the first layer's coordnate system, so if you add the geographic one fist it will be geographic.
To make them be the same use the Project Geoprocessing Tool then there wont be a problem. Note: if the transformation dialog came up when you added the second layer you will need to supply a transformation also for the project dialog.
The same thing would happen - the projected CRS would be reprojected on the fly to the GCS.
With a new dataframe, the projection is set to the first layer added with a defined projection. All subsequent layers added, if different, will be reprojected to the dataframe's projection. Note a transformation may be required if the CRS datums differ, which should trip a warning message unless you've disabled that.
Steps for proper fit is going to depend on what data you have and what you're doing with it. Most likely you'll want a projected CRS for your dataframe and have the GCS data reprojected to that. There are tools to permanently reproject a dataset (note, there is a difference between DEFINE and PROJECT).