Even the smallest city airport is going to have most of the peripheral services that are common in the big international airports. For instance, car rental companies will have their offices near the airport and, while there may not be a large selection of rental cars, most of the more popular models will be available. Similarly, a smaller city airport coach hire service will likely have many less employees available to support you but the basic service of picking you up and delivering you where you want to go will be provided.
Whatever airport you are arriving at, the general layout is the same and your city airport coach hire is going to be meeting you somewhere around the luggage carousel. Before the introduction of all of the security controls, the city airport coach hire would have met you as you come out of the jet way and would have assisted you with your carry-on luggage as well as directing you to the luggage carousel.
Of course, with the controlled access to certain spaces within airports today, your ride will be waiting for you as you enter the area where you can claim your luggage and step out into the world. Of course, if you have not made arrangements with the city airport coach hire service then you will need to locate their service desk within the airport itself. Usually there is a well-marked area where all of the various shuttles and transportation companies maintain a communal service operation.
They will be able to assist you as long as you know the name of your hotel or destination and have a credit card to charge their services to. At that point, the chauffeur will ask you to wait by the door or sidewalk and he will go to get his vehicle to pick you up.