Since you have not stated anything about seat or type of checkride, I run your throught the IFRMEL requirements, since that is what I am most familar with.
As a check airman, I am notified by either the Chief Pilot or the Training Department that you are ready for a check ride. Then I examine your pilot file (training records). I am looking for many different things. Making sure everything has been done in accordance with the training program. All the boxes are filled. The i's dotted and the t's crossed, etc. Then I schedule a date and time for the checkride. Co-ordinating with maintenance and operations on aircraft availablility.
Next I notify the company's Principle Operations Inspector (FAA) that I will be conducting a checkride with you on this date and time. All my Letters of Authorization have required this notification. So the FAA can observe the check ride. Don't worry about it. I'll discuss it a little later.
On the day of the checkride, I will met with you and ask for your pilot certificate, medical and driver's license. While I am making copies for my files, I have you do a couple of written tests. Performance and regulations. Check airman may give you written test in leu of or in combination with an oral exam. I use both.
We will then discuss the Operations Manual and Operations Specificiations. Followed by the regulations, Parts 1, 61, 91, 135 and 830. Depending on your experience level, the aircraft and seat, I might discuss Part 25 with, mostly performance areas, 67, 71, 97 and 119. Usually just lightly and just a discussion.
We will then talk about the aircraft. Systems, limitations, normal and emergency procedures.
I will ask a question or two that are thinking type questions. No real right answer. Just to get you thinking. They are not gotcha questions, these are things that have really happened.
Finally, I will have you file a file plan and we will go fly.
I am going to watch you preflight the aircraft. I might ask a question or two. More likely on an initial.
You will do the checklists, start, taxi and do pre-takeof checks.
For take off's you will have a normal, a cross wind, rejected and a power plant failure. Captain must do an instrument TO. Manuvers can be combined.
We will do an area departure. And then do some airwork. FO's are not required to be tested for steep turns. And not required for recurrent. However, I have new hire FO's do them. It tends to loosen then up a bit. The into stalls. All three. Clean, TO and departure and Landing configuration. Followed by unusual attitudes. And depending on the aircraft maybe emergency descents.
After an area arrival, we will do a normal ILS, engine out ILS with a miss, coupled approach, 2 non-precision approaches, one of which will be circling. The FO is not required to do an engine out ILS, couple approach, missed approach for an ILS, a 2nd non-precision approach or a circling approach. Normally, because of all the different types of approaches we do, I generally have the FO's do the single engine ILS and a 2nd non-precision approach.
Then back home. The pilot will have also completed a normal landing, crosswind landing, landing from an ILS, Engine out landing, rejected landing and a no flap landing.
Also during this ride, I will asking questions as we go along and from time to time giving you system malfunctions.
After we get back to the ramp, you will close out the paperwork and we will discuss the ride. How you did and what you need to work on. I will not sugar coat it.
The only real difference between an initial or a recurrent, is that a recurrent might seem a little bit less involved. It really isn't. Since I am also a line Captain, I am regularly flying with these pilots and observing them. So I am seeing many of the required items on a daily basis. So I will cover those items, but not in the detail of an inital. Don't get me wrong, the items are covered, but a little bit differently. For example, I flew with another Captain into Aspen, yesterday. G+He did the performance planning for the leg out. If I were giving him a check ride today, I would ask him about the performance planning he did yesterday. Things like, what was the limiting factor for the takeoff yesterday?
Now during the checkride, I saw anything sub standard, I can stop the checkride and conduct training. It is my option. It depends on what I saw.
Once back inside, I start writting up Form 8410. A copy goes in your file, you get the top copy and a copy goes in my check airman file.
As for the feds riding along, they observe check airmen at least once a year. Depending on how many checkrides they conduct. Don't worry, ignore them. They are actually checking me. I know that is easier said than done.
Hope that helps. Good luck.