Which car to board on train from Inverness to Glasgow via Perth?

As the message gives Coach A, you can be sure that the coaches are given letters rather than numbers. So you get in at coach A, and on the platform there should be information where the coach will be on the platform, if not in text on the platform, it might well be called out when they announce the train. (In some countries you get it with your phone app details by now, not heard that in the UK yet.)
If you are not familiar with the word 'coach' for a train, it means one of the carriages or cars of the train.
The letter A, (as in other trains the number 1) is most likely to be on one end of the train. This train is likely to start where you join it and if so, it will sit on the platform longer than when it stops at other stations. Which in turn allows you more time to find your coach and seat. But do keep an eye on the time, the train will go when it is time, whether you are in or not.
As a rule there is a message on or near the door of a train with the number/letter of the coach and sometimes its destination. The numbers in most trains are in order, so you can follow from the middle of the train by looking at two doors.

In the normal trains from Glasgow to Edinburgh there are no reserved seats.
So you can enter the train in any of the second class coaches. (I do not remember whether there are first class or whatever they call them, there might not be any.) For these trains, if the train has an other class, it will be mentioned when the train is announced. Mostly as 'first class coaches will be at the head of the train'. Again, it is very likely that you will enter the train when it is waiting on the platform, at the start of its journey. Giving you more time to find your way around.

In any case, ask the people around you on the platform, in uniform if there, just other passengers if you see no uniforms. Most people do know the answers for you.