The A/C specialist will check for a freon leak. This will determine the extent of your repair. If the leak is a hose or a fitting, the cost will be much less then if the leak were coming from the evaporator, the condensor, or the A/C compressor. In any event, a leak should be fixed. Adding freon occasionally will get the system to blow cold air, but will only leak out again. If it's a slow leak, perhaps charging the system (adding freon) will work for 2 days, 2 weeks, 2 months, or perhaps longer. The specialist you took it to will tell you, but its best to simply repair the component that's leaking.
They will want to replace the dryer in most cases when working on an A/C system; the dryer removes moisture from the A/C system, and a leak can draw in moisture from the outside air, and damage the A/C compressor, a reason why you want to identify and repair the leak.
To learn on how an automobile A/C system works and their components, google "automotive A/C". You will find good articles and write ups on how they work, and good descriptions on their components.
keep us posted as to your findings. Good luck!
It is better to keep your mouth closed and let people think you are a fool than to open it and remove all doubt.