As far as the check portion, I usually listen to the aid first with a stethoscope, cycle thru the programs (if aid has a program button) and volume control (if it has one) to make sure everything functions correctly. Some aids have internal type wax guards as well that I look at to see if they need replacing or cleaning. This usually requires disassembling the hearing aid to its core and is not advisable for patients to do themselves. At the same time I am looking for any moisture that may have built up.
I usually tell my patients checking and cleaning is like changing the oil on your car every 3-5k miles. The better regular preventive maintenance we do, the better you will hear and the longer your hearing aid will last. I do not charge for checkups and cleanings for just that reason.
Hope this helps!